Edit Profile (opens in new tab) Gerdzhikov, Vladimir Stefanov Compute Distance To: Compute Author ID: gerdzhikov.vladimir-stefanov Published as: Gerdjikov, V. S.; Gerdjikov, Vladimir S.; Gerdjikov, Vladimir; Gerdzhikov, V. S.; Gerdjikov, Vladimir Stefanov; Gerdjikov, V. more...less Further Spellings: Gerjikov, Vladimir Stefanov Homepage: http://www.inrne.bas.bg/index.php/scg/vladimir-gerdjikov External Links: ORCID · Google Scholar · ResearchGate · Math-Net.Ru · dblp Documents Indexed: 128 Publications since 1980, including 2 Books 2 Contributions as Editor Co-Authors: 49 Co-Authors with 110 Joint Publications 812 Co-Co-Authors all top 5 Co-Authors 19 single-authored 30 Kostov, Nikolay A. 21 Grahovski, Georgi G. 16 Valchev, Tihomir I. 12 Ivanov, Rossen I. 11 Kyuldjiev, Assen V. 9 Ivanov, Maksim I. 8 Kulish, Petr Petrovich 8 Stefanov, Aleksander A. 8 Vilasi, Gaetano 7 Todorov, Michail D. 6 Marmo, Giuseppe 6 Mikhailov, Alexander Vasil’evich 5 Kaup, David J. 5 Yanovski, Alexandar Borissov 4 Evstatiev, Evstati G. 4 Mladenov, Dimitar M. 4 Uzunov, Ivan M. 4 Varbev, Stanislav K. 3 Atanasov, Victor A. 2 Constantin, Adrian 2 Constantinescu, Radu D. 2 Doktorov, Evgeny V. 2 Gadzhiev, I. T. 2 Khristov, Evgeni Khristov 2 Matsuka, N. P. 2 Matveev, Vladimir B. 2 Pavlov, Maxim V. 2 Salerno, Mario 2 Sekigawa, Kouei 2 Smirnov, Alexander O. 1 Babalic, Corina N. 1 Babalic, N. C. 1 Baizakov, Bakhtiyor B. 1 Boyadjiev, G. P. 1 Dandoloff, Rossen 1 Diankov, G. L. 1 Dimiev, Stancho G. 1 Enolskiĭ, Viktor Zelikovich 1 Grahavoski, G. G. 1 Grahovshi, G. G. 1 Iliev, Iliya Dimov 1 Konotop, Vladimir V. 1 Kostova, Zoia 1 Lederer, Falk 1 Matsushita, Yasuo 1 Mioc, Vasile 1 Mladenov, Ivaĭlo M. 1 Vaklev, Y. S. 1 Yanovskij, A. B. all top 5 Serials 12 Theoretical and Mathematical Physics 9 Journal of Geometry and Symmetry in Physics 6 Inverse Problems 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Journal of Mathematical Physics 3 Wave Motion 3 Journal of Soviet Mathematics 3 Physica D 3 Journal of Physics A: Mathematical and General 3 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 2 Bulgarian Journal of Physics 2 Mathematics and Computers in Simulation 2 Journal of Nonlinear Mathematical Physics 2 Lecture Notes in Physics 2 Journal of Physics A: Mathematical and Theoretical 2 PLISKA. Studia Mathematica 1 Communications in Mathematical Physics 1 Letters in Mathematical Physics 1 Mathematical Notes 1 Matematicheskie Zametki 1 Nonlinearity 1 Physics Letters. A 1 Teoreticheskaya i Matematicheskaya Fizika 1 Studies in Applied Mathematics 1 Applied Numerical Mathematics 1 Discrete and Continuous Dynamical Systems 1 Balkan Journal of Geometry and its Applications (BJGA) 1 Communications on Pure and Applied Analysis 1 AIP Conference Proceedings 1 Discrete and Continuous Dynamical Systems. Series S 1 Proceedings of the Estonian Academy of Sciences 1 Journal of Geometric Mechanics 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Journal of Siberian Federal University. Mathematics & Physics all top 5 Fields 101 Partial differential equations (35-XX) 88 Dynamical systems and ergodic theory (37-XX) 20 Quantum theory (81-XX) 18 Nonassociative rings and algebras (17-XX) 14 Statistical mechanics, structure of matter (82-XX) 12 Optics, electromagnetic theory (78-XX) 9 Ordinary differential equations (34-XX) 7 Mechanics of particles and systems (70-XX) 6 Differential geometry (53-XX) 4 General and overarching topics; collections (00-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Mechanics of deformable solids (74-XX) 3 Topological groups, Lie groups (22-XX) 3 Operator theory (47-XX) 2 Group theory and generalizations (20-XX) 2 Functions of a complex variable (30-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Fluid mechanics (76-XX) 1 Algebraic geometry (14-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 88 Publications have been cited 736 times in 440 Documents Cited by ▼ Year ▼ Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I. 212 2006 Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147Gerdjikov, V. S.; Saxena, A. 37 2017 The quadratic bundle of general form and the nonlinear evolution equations. II: Hierarchies of structures. Zbl 0522.35082Gerdzhikov, V. S.; Ivanov, M. I. 37 1983 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Zbl 1167.37001Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 34 2008 The generating operator for the n \(\times n\) linear system. Zbl 1194.35365Gerdjikov, V. S.; Kulish, P. P. 22 1981 Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086Gerdzhikov, V. S. 21 1986 The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I. 18 2016 Quadratic bundle and nonlinear equations. Zbl 0454.35071Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 17 1981 Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I. 16 2007 Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system. Zbl 0814.34070Gerdjikov, V. S.; Yanovski, A. B. 15 1994 \(N\)-wave interactions related to simple Lie algebras. \(\mathbb{Z}_2\)-reductions and soliton solutions. Zbl 0988.35143Gerdjikov, V. S.; Grahavoski, G. G.; Ivanov, R. I.; Kostov, N. A. 15 2001 Algebraic and analytic aspects of soliton type equations. Zbl 1026.37059Gerdjikov, Vladimir S. 14 2002 Reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. I: \(\mathbb Z_2\)-reductions. Zbl 1001.37074Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 12 2001 Expansions over the ”squared” solutions and difference evolution equations. Zbl 0554.35118Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 12 1984 Gauge covariant theory of the generating operator. I. Zbl 0611.35082Gerdzhikov, V. S.; Yanovskij, A. B. 12 1986 Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326Gerdjikov, V. S.; Kostov, N. A.; Valchev, T. I. 10 2009 Multicomponent NLS-type equations on symmetric spaces and their reductions. Zbl 1178.35347Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 10 2005 Stability and quasi-equidistant propagation of NLS soliton trains. Zbl 0948.81658Gerdjikov, V. S.; Evstatiev, E. G.; Kaup, D. J.; Diankov, G. L.; Uzunov, I. M. 10 1998 Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I. 8 2010 Basic aspects of soliton theory. Zbl 1086.35102Gerdjikov, Vladimir S. 8 2005 On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations. Zbl 0524.34029Gerdzhikov, V. S. 8 1982 Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces. Zbl 1248.37065Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Mikhailov, Alexander V.; Valchev, Tihomir I. 7 2011 \(N\)-soliton train and generalized complex Toda chain for the Manakov system. Zbl 1142.37041Gerdjikov, V. S.; Doktorov, E. V.; Matsuka, N. P. 7 2007 Quadratic bundle and nonlinear equations. Zbl 0439.35055Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 7 1980 On the \(N\)-wave equations and soliton interactions in two and three dimensions. Zbl 1365.35151Gerdjikov, V. S.; Ivanov, R. I.; Kyuldjiev, A. V. 7 2011 Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020Gerdjikov, V. S.; Uzunov, I. M. 6 2001 Two-component Bose-Einstein condensates in optical lattices. Zbl 1099.35529Kostov, N. A.; Gerdjikov, V. S.; Enol’skii, V. Z.; Salerno, M.; Konotop, V. V. 6 2004 CBC systems with Mikhailov reductions by Coxeter automorphism. I: Spectral theory of the recursion operators. Zbl 1311.35247Gerdjikov, V. S.; Yanovski, A. B. 6 2015 Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose-Einstein mixtures. Zbl 1251.35147Gerdjikov, V. S.; Kostov, N. A.; Doktorov, E. V.; Matsuka, N. P. 5 2009 The complex Toda chains and the simple Lie algebras – solutions and large time asymptotics. Zbl 0952.37049Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I. 5 1998 Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101Gerdjikov, Vladimir S.; Grahovski, Georgi G. 5 2010 On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I. 5 2017 The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108Gerdjikov, V. S. 4 1994 Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A. 4 2019 Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326Gerdjikov, V. S. 4 2017 \(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129Gerdjikov, V. S. 4 1990 On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184Gerdjikov, Vladimir S.; Kostov, Nikolay A. 4 2008 On classification of soliton solutions of multicomponent nonlinear evolution equations. Zbl 1143.37048Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I. 4 2008 Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M. 4 2005 On soliton equations with \(\mathbb{Z}_h\) and \(\mathbb{D}_h\) reductions: conservation laws and generating operators. Zbl 1293.35268Gerdjikov, Vladimir S.; Yanovski, Alexandar B. 4 2013 \(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 3 2002 Construction of real forms of complexified Hamiltonian dynamical systems. Zbl 1053.37031Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G. 3 2003 mKdV-type of equations related to \(B_2^{(1)}\) and \(A_4^{(2)}\). Zbl 1338.35392Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 3 2015 Gauge transformations and generating operators for the discrete Zakharov- Shabat system. Zbl 0618.35103Gerdzhikov, V. S.; Ivanov, M. I.; Vaklev, Y. S. 3 1986 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 3 2010 Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. Zbl 0568.35084Gerdzhikov, V. S.; Kulish, P. P. 3 1985 Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050Gerdjikov, V. S.; Ivanov, M. I. 3 1992 Fordy-Kulish model and spinor Bose-Einstein condensate. Zbl 1163.82006Atanasov, V. A.; Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 3 2008 The Manakov system as two moving interacting curves. Zbl 1142.35086Kostov, N. A.; Dandoloff, R.; Gerdjikov, V. S.; Grahovski, G. G. 3 2007 Exact solutions for equations of Bose-Fermi mixtures in one-dimensional optical lattice. Zbl 1139.82316Kostov, Nikolay A.; Gerdjikov, Vladimir S.; Valchev, Tihomir I. 3 2007 On the multi-component NLS type equations on symmetric spaces: reductions and soliton solutions. Zbl 1079.53075Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A. 3 2005 \(N\)-soliton interactions for the Manakov system: effects of external potentials. Zbl 1326.35343Gerdjikov, V. S.; Todorov, M. D. 3 2014 Manakov solitons and effects of external potential wells. Zbl 1336.35325Todorov, M. D.; Kyuldjiev, A. V.; Gerdjikov, V. S. 3 2015 Lax representation does not mean complete integrability. Zbl 0941.35540Gerdjikov, V. S. 2 1992 The complex Toda chains and the simple Lie algebras. II: Explicit solutions and asymptotic behaviour. Zbl 0952.37048Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I. 2 2000 Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions! Zbl 1053.37062Gerdjikov, V. S. 2 2003 Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I. 2 2010 \(N\)-wave equations with orthogonal algebras: \(\mathbb Z_2\) and \(\mathbb Z_2\times\mathbb Z_2\) reductions and soliton solutions. Zbl 1134.37028Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Valchev, Tihomir I. 2 2007 Breather solutions of \(N\)-wave equations. Zbl 1123.35342Gerdjikov, Vladimir; Valchev, Tihomir 2 2007 How many types of soliton solutions do we know? Zbl 1101.35069Gerdjikov, Vladimir S.; Kaup, David J. 2 2006 New integrable multi-component NLS type equations on symmetric spaces: \(\mathbb Z_4\) and \(\mathbb Z_6\) reductions. Zbl 1101.35070Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Atanasov, Victor A. 2 2006 Exact solutions for a class of integrable Hénon-Heiles-type systems. Zbl 1309.70014Kostov, N. A.; Gerdjikov, V. S.; Mioc, V. 2 2010 Integrable equations and recursion operators related to the affine Lie algebras \(A_r^{(1)}\). Zbl 1317.35218Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 2 2015 On the soliton solutions of a family of Tzitzeica equations. Zbl 1325.35188Babalic, Corina N.; Constantinescu, Radu; Gerdjikov, Vladimir S. 2 2015 New types of two component NLS-type equations. Zbl 1389.35290Gerdjikov, Vladimir; Stefanov, Aleksander 2 2016 Multisoliton interactions for the Manakov system under composite external potentials. Zbl 1330.35429Todorov, Michail; Gerdjikov, Vladimir S.; Kyuldjiev, Assen V. 2 2015 On mKdV equations related to the affine Kac-Moody algebra \(A_5^{(2)}\). Zbl 1343.35208Gerdjikov, Vladimir S.; Mladenov, Dimitar M.; Stefanov, Aleksander A.; Varbev, Stanislav K. 2 2015 On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. Zbl 0522.35083Gerdzhikov, V. S.; Kulish, P. P. 2 1983 Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras \(D_4^{(1)}\), \(D_4^{(2)}\), and \(D_4^{(3)}\). Zbl 1456.37072Gerdjikov, V. S.; Stefanov, A. A.; Iliev, I. D.; Boyadjiev, G. P.; Smirnov, A. O.; Matveev, V. B.; Pavlov, M. V. 2 2020 Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations. Zbl 0802.35137Gerdjikov, V. S. 1 1992 The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 07364291Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 1 2021 Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir 1 2010 Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199Gerdjikov, Vladimir S. 1 2011 Bose-Einstein condensates and multi-component NLS models on symmetric spaces of BD. I-type. Expansions over squared solutions. Zbl 1218.37100Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I. 1 2011 Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type. Zbl 1157.37335Gerdjikov, Vladimir S.; Kostov, Nikolay A. 1 2008 On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions. Zbl 1205.35292Gerdjikov, Vladimir S. 1 2009 On soliton interactions for the hierarchy of a generalised Heisenberg ferromagnetic model on \(SU (3)/ S (U (1) \times U (2))\) symmetric space. Zbl 1259.82127Gerdjikov, Vladimir; Grahovski, Georgi; Mikhailov, Alexander; Valchev, Tihomir 1 2012 Soliton equations with deep reductions. Generalized Fourier transforms. Zbl 1180.35444Gerdjikov, V.; Kostov, N.; Valchev, T. 1 2007 On the multi-component NLS type systems and their gauge equivalent: examples and reductions. Zbl 1116.35355Gerdjikov, V. S.; Grahovski, G. G. 1 2004 On the multi-component nonlinear Schrödinger equation with constant boundary conditions. Zbl 1120.81022Atanasov, Victor; Gerdjikov, Vladimir 1 2006 Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil. Zbl 0597.35112Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. 1 1986 On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522Gerdjikov, V. S.; Grahovski, G. G. 1 2004 On expansions in products of solutions of two Dirac systems. Zbl 0448.34025Gerdzhikov, V. S.; Khristov, E. Kh. 1 1980 The expansion in ”square” of eigenfunctions of a matrix linear system. Zbl 0469.34015Gerdzhikov, V. S.; Kulish, P. P. 1 1980 Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142Gerdjikov, Vladimir S.; Grahovski, Georgi G. 1 2010 Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle. Zbl 0514.35078Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. 1 1982 The quadratic bundle of a general form and the nonlinear evolution equations. I: Expansions over the ”squared” solutions: generalized Fourier transform. Zbl 0522.35081Gerdzhikov, V. S.; Ivanov, M. I. 1 1983 Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V. 1 2017 The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 07364291Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 1 2021 Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras \(D_4^{(1)}\), \(D_4^{(2)}\), and \(D_4^{(3)}\). Zbl 1456.37072Gerdjikov, V. S.; Stefanov, A. A.; Iliev, I. D.; Boyadjiev, G. P.; Smirnov, A. O.; Matveev, V. B.; Pavlov, M. V. 2 2020 Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A. 4 2019 Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147Gerdjikov, V. S.; Saxena, A. 37 2017 On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I. 5 2017 Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326Gerdjikov, V. S. 4 2017 Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V. 1 2017 The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I. 18 2016 New types of two component NLS-type equations. Zbl 1389.35290Gerdjikov, Vladimir; Stefanov, Aleksander 2 2016 CBC systems with Mikhailov reductions by Coxeter automorphism. I: Spectral theory of the recursion operators. Zbl 1311.35247Gerdjikov, V. S.; Yanovski, A. B. 6 2015 mKdV-type of equations related to \(B_2^{(1)}\) and \(A_4^{(2)}\). Zbl 1338.35392Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 3 2015 Manakov solitons and effects of external potential wells. Zbl 1336.35325Todorov, M. D.; Kyuldjiev, A. V.; Gerdjikov, V. S. 3 2015 Integrable equations and recursion operators related to the affine Lie algebras \(A_r^{(1)}\). Zbl 1317.35218Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 2 2015 On the soliton solutions of a family of Tzitzeica equations. Zbl 1325.35188Babalic, Corina N.; Constantinescu, Radu; Gerdjikov, Vladimir S. 2 2015 Multisoliton interactions for the Manakov system under composite external potentials. Zbl 1330.35429Todorov, Michail; Gerdjikov, Vladimir S.; Kyuldjiev, Assen V. 2 2015 On mKdV equations related to the affine Kac-Moody algebra \(A_5^{(2)}\). Zbl 1343.35208Gerdjikov, Vladimir S.; Mladenov, Dimitar M.; Stefanov, Aleksander A.; Varbev, Stanislav K. 2 2015 \(N\)-soliton interactions for the Manakov system: effects of external potentials. Zbl 1326.35343Gerdjikov, V. S.; Todorov, M. D. 3 2014 On soliton equations with \(\mathbb{Z}_h\) and \(\mathbb{D}_h\) reductions: conservation laws and generating operators. Zbl 1293.35268Gerdjikov, Vladimir S.; Yanovski, Alexandar B. 4 2013 On soliton interactions for the hierarchy of a generalised Heisenberg ferromagnetic model on \(SU (3)/ S (U (1) \times U (2))\) symmetric space. Zbl 1259.82127Gerdjikov, Vladimir; Grahovski, Georgi; Mikhailov, Alexander; Valchev, Tihomir 1 2012 Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces. Zbl 1248.37065Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Mikhailov, Alexander V.; Valchev, Tihomir I. 7 2011 On the \(N\)-wave equations and soliton interactions in two and three dimensions. Zbl 1365.35151Gerdjikov, V. S.; Ivanov, R. I.; Kyuldjiev, A. V. 7 2011 Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199Gerdjikov, Vladimir S. 1 2011 Bose-Einstein condensates and multi-component NLS models on symmetric spaces of BD. I-type. Expansions over squared solutions. Zbl 1218.37100Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I. 1 2011 Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I. 8 2010 Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101Gerdjikov, Vladimir S.; Grahovski, Georgi G. 5 2010 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 3 2010 Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I. 2 2010 Exact solutions for a class of integrable Hénon-Heiles-type systems. Zbl 1309.70014Kostov, N. A.; Gerdjikov, V. S.; Mioc, V. 2 2010 Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir 1 2010 Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142Gerdjikov, Vladimir S.; Grahovski, Georgi G. 1 2010 Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326Gerdjikov, V. S.; Kostov, N. A.; Valchev, T. I. 10 2009 Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose-Einstein mixtures. Zbl 1251.35147Gerdjikov, V. S.; Kostov, N. A.; Doktorov, E. V.; Matsuka, N. P. 5 2009 On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions. Zbl 1205.35292Gerdjikov, Vladimir S. 1 2009 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Zbl 1167.37001Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 34 2008 On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184Gerdjikov, Vladimir S.; Kostov, Nikolay A. 4 2008 On classification of soliton solutions of multicomponent nonlinear evolution equations. Zbl 1143.37048Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I. 4 2008 Fordy-Kulish model and spinor Bose-Einstein condensate. Zbl 1163.82006Atanasov, V. A.; Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 3 2008 Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type. Zbl 1157.37335Gerdjikov, Vladimir S.; Kostov, Nikolay A. 1 2008 Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I. 16 2007 \(N\)-soliton train and generalized complex Toda chain for the Manakov system. Zbl 1142.37041Gerdjikov, V. S.; Doktorov, E. V.; Matsuka, N. P. 7 2007 The Manakov system as two moving interacting curves. Zbl 1142.35086Kostov, N. A.; Dandoloff, R.; Gerdjikov, V. S.; Grahovski, G. G. 3 2007 Exact solutions for equations of Bose-Fermi mixtures in one-dimensional optical lattice. Zbl 1139.82316Kostov, Nikolay A.; Gerdjikov, Vladimir S.; Valchev, Tihomir I. 3 2007 \(N\)-wave equations with orthogonal algebras: \(\mathbb Z_2\) and \(\mathbb Z_2\times\mathbb Z_2\) reductions and soliton solutions. Zbl 1134.37028Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Valchev, Tihomir I. 2 2007 Breather solutions of \(N\)-wave equations. Zbl 1123.35342Gerdjikov, Vladimir; Valchev, Tihomir 2 2007 Soliton equations with deep reductions. Generalized Fourier transforms. Zbl 1180.35444Gerdjikov, V.; Kostov, N.; Valchev, T. 1 2007 Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I. 212 2006 How many types of soliton solutions do we know? Zbl 1101.35069Gerdjikov, Vladimir S.; Kaup, David J. 2 2006 New integrable multi-component NLS type equations on symmetric spaces: \(\mathbb Z_4\) and \(\mathbb Z_6\) reductions. Zbl 1101.35070Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Atanasov, Victor A. 2 2006 On the multi-component nonlinear Schrödinger equation with constant boundary conditions. Zbl 1120.81022Atanasov, Victor; Gerdjikov, Vladimir 1 2006 Multicomponent NLS-type equations on symmetric spaces and their reductions. Zbl 1178.35347Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 10 2005 Basic aspects of soliton theory. Zbl 1086.35102Gerdjikov, Vladimir S. 8 2005 Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M. 4 2005 On the multi-component NLS type equations on symmetric spaces: reductions and soliton solutions. Zbl 1079.53075Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A. 3 2005 Two-component Bose-Einstein condensates in optical lattices. Zbl 1099.35529Kostov, N. A.; Gerdjikov, V. S.; Enol’skii, V. Z.; Salerno, M.; Konotop, V. V. 6 2004 On the multi-component NLS type systems and their gauge equivalent: examples and reductions. Zbl 1116.35355Gerdjikov, V. S.; Grahovski, G. G. 1 2004 On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522Gerdjikov, V. S.; Grahovski, G. G. 1 2004 Construction of real forms of complexified Hamiltonian dynamical systems. Zbl 1053.37031Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G. 3 2003 Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions! Zbl 1053.37062Gerdjikov, V. S. 2 2003 Algebraic and analytic aspects of soliton type equations. Zbl 1026.37059Gerdjikov, Vladimir S. 14 2002 \(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 3 2002 \(N\)-wave interactions related to simple Lie algebras. \(\mathbb{Z}_2\)-reductions and soliton solutions. Zbl 0988.35143Gerdjikov, V. S.; Grahavoski, G. G.; Ivanov, R. I.; Kostov, N. A. 15 2001 Reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. I: \(\mathbb Z_2\)-reductions. Zbl 1001.37074Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 12 2001 Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020Gerdjikov, V. S.; Uzunov, I. M. 6 2001 The complex Toda chains and the simple Lie algebras. II: Explicit solutions and asymptotic behaviour. Zbl 0952.37048Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I. 2 2000 Stability and quasi-equidistant propagation of NLS soliton trains. Zbl 0948.81658Gerdjikov, V. S.; Evstatiev, E. G.; Kaup, D. J.; Diankov, G. L.; Uzunov, I. M. 10 1998 The complex Toda chains and the simple Lie algebras – solutions and large time asymptotics. Zbl 0952.37049Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I. 5 1998 Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system. Zbl 0814.34070Gerdjikov, V. S.; Yanovski, A. B. 15 1994 The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108Gerdjikov, V. S. 4 1994 Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050Gerdjikov, V. S.; Ivanov, M. I. 3 1992 Lax representation does not mean complete integrability. Zbl 0941.35540Gerdjikov, V. S. 2 1992 Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations. Zbl 0802.35137Gerdjikov, V. S. 1 1992 \(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129Gerdjikov, V. S. 4 1990 Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086Gerdzhikov, V. S. 21 1986 Gauge covariant theory of the generating operator. I. Zbl 0611.35082Gerdzhikov, V. S.; Yanovskij, A. B. 12 1986 Gauge transformations and generating operators for the discrete Zakharov- Shabat system. Zbl 0618.35103Gerdzhikov, V. S.; Ivanov, M. I.; Vaklev, Y. S. 3 1986 Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil. Zbl 0597.35112Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. 1 1986 Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. Zbl 0568.35084Gerdzhikov, V. S.; Kulish, P. P. 3 1985 Expansions over the ”squared” solutions and difference evolution equations. Zbl 0554.35118Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 12 1984 The quadratic bundle of general form and the nonlinear evolution equations. II: Hierarchies of structures. Zbl 0522.35082Gerdzhikov, V. S.; Ivanov, M. I. 37 1983 On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. Zbl 0522.35083Gerdzhikov, V. S.; Kulish, P. P. 2 1983 The quadratic bundle of a general form and the nonlinear evolution equations. I: Expansions over the ”squared” solutions: generalized Fourier transform. Zbl 0522.35081Gerdzhikov, V. S.; Ivanov, M. I. 1 1983 On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations. Zbl 0524.34029Gerdzhikov, V. S. 8 1982 Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle. Zbl 0514.35078Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. 1 1982 The generating operator for the n \(\times n\) linear system. Zbl 1194.35365Gerdjikov, V. S.; Kulish, P. P. 22 1981 Quadratic bundle and nonlinear equations. Zbl 0454.35071Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 17 1981 Quadratic bundle and nonlinear equations. Zbl 0439.35055Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 7 1980 On expansions in products of solutions of two Dirac systems. Zbl 0448.34025Gerdzhikov, V. S.; Khristov, E. Kh. 1 1980 The expansion in ”square” of eigenfunctions of a matrix linear system. Zbl 0469.34015Gerdzhikov, V. S.; Kulish, P. P. 1 1980 all cited Publications top 5 cited Publications all top 5 Cited by 472 Authors 34 Gerdzhikov, Vladimir Stefanov 21 Yin, Zhaoyang 20 Mi, Yongsheng 18 Mu, Chunlai 15 Zhou, Shouming 12 Ivanov, Rossen I. 11 Guo, Boling 11 Liu, Yue 11 Qiao, Zhijun 10 Ma, Wen-Xiu 9 Gürses, Metin 8 Grahovski, Georgi G. 8 Pekcan, Asli 8 Qu, Changzheng 8 Shepelsky, Dmitry 7 Fan, Engui 7 Kostov, Nikolay A. 7 Shen, Chunyu 7 Tian, Lixin 7 Valchev, Tihomir I. 6 Chen, Yong 6 Guo, Yingying 6 Yan, Zhenya 5 Boutet de Monvel, Anne Marie 5 Gao, Anna 5 Lai, Shaoyong 5 Todorov, Michail D. 5 Zheng, Rudong 4 Constantin, Adrian 4 Fokas, Athanassios S. 4 Geng, Xianguo 4 Guo, Zhengguang 4 Huang, Daiwen 4 Li, Nianhua 4 Liu, Xiaochuan 4 Liu, Zhengrong 4 Luo, Ting 4 Sakhnovich, Alexander L. 4 Yang, Jianke 4 Zhang, Guoqiang 4 Zhang, Ling 4 Zhu, Mingxuan 3 Chen, Rong 3 Christov, Ognyan 3 Doungmo Goufo, Emile Franc 3 Duruk Mutlubaş, Nilay 3 Fu, Ying 3 Geyer, Anna 3 Guha, Partha 3 Gui, Guilong 3 He, Bin 3 He, Jingsong 3 Henry, David 3 Hu, Beibei 3 Ionescu-Kruse, Delia 3 Ivanov, Aleksandr S. 3 Jiang, Zaihong 3 Kulish, Petr Petrovich 3 Kyuldjiev, Assen V. 3 Matveev, Vladimir B. 3 Moon, Byungsoo 3 Mukherjee, Indranil 3 Mustafa, Octavian G. 3 Myrzakulov, Ratbay 3 Olver, Peter John 3 Prinari, Barbara 3 Qiu, Deqin 3 Rybalko, Yan 3 Senthilvelan, Murugaian 3 Smirnov, Alexander O. 3 Stefanov, Aleksander A. 3 Xia, Baoqiang 3 Xu, Jian 3 Yang, Shaojie 3 Zhang, Baoshuai 3 Zhu, Min 2 Arnaudon, Alexis 2 Bogolyubov, Nikolaĭ Mikhaĭlovich 2 Carroll, Robert Wayne 2 Chen, Jinbing 2 Cheng, Wenguang 2 Cheng, Yi 2 Chow, Kwok Wing 2 Chung, Won-Sang 2 Demontis, Francesco 2 Doktorov, Evgeny V. 2 Dong, Huanhe 2 Eckhardt, Jonathan 2 Escher, Joachim 2 Feng, Baofeng 2 Gongye, Yingyin 2 Guan, Chunxia 2 Hakkaev, Sevdzhan A. 2 Han, Jingwei 2 He, Huijun 2 Hou, Yu 2 Iliev, Iliya Dimov 2 Kang, Jing 2 Kaup, David J. 2 Kolev, Boris ...and 372 more Authors all top 5 Cited in 102 Serials 36 Journal of Mathematical Physics 28 Theoretical and Mathematical Physics 24 Journal of Nonlinear Mathematical Physics 22 Journal of Differential Equations 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Discrete and Continuous Dynamical Systems 14 Physics Letters. A 14 Physica D 13 Communications in Mathematical Physics 13 Wave Motion 12 Applicable Analysis 10 Journal of Mathematical Analysis and Applications 10 Monatshefte für Mathematik 10 Nonlinear Dynamics 9 Communications in Nonlinear Science and Numerical Simulation 7 Journal of Geometry and Physics 7 Applied Mathematics Letters 7 Nonlinear Analysis. Real World Applications 6 Applied Mathematics and Computation 6 Studies in Applied Mathematics 6 Journal of Nonlinear Science 5 Letters in Mathematical Physics 5 Chaos, Solitons and Fractals 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Abstract and Applied Analysis 5 Journal of Mathematical Fluid Mechanics 5 Advances in Mathematical Physics 4 Journal of Soviet Mathematics 4 Mathematical Physics, Analysis and Geometry 4 Boundary Value Problems 3 International Journal of Theoretical Physics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Computational and Applied Mathematics 3 International Journal of Geometric Methods in Modern Physics 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Ufimskiĭ Matematicheskiĭ Zhurnal 2 Archive for Rational Mechanics and Analysis 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 Nuclear Physics. B 2 Reports on Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Advances in Mathematics 2 Journal of Functional Analysis 2 Quarterly of Applied Mathematics 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Journal of Mathematical Sciences (New York) 2 Mathematical Problems in Engineering 2 Chaos 2 Differential Equations 2 Journal of Evolution Equations 2 Discrete and Continuous Dynamical Systems. Series B 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Advances in Difference Equations 2 Frontiers of Mathematics in China 2 Journal of Physics A: Mathematical and Theoretical 2 International Journal of Applied and Computational Mathematics 1 Modern Physics Letters A 1 Modern Physics Letters B 1 International Journal of Modern Physics B 1 Mathematical Notes 1 Reviews in Mathematical Physics 1 Annales de l’Institut Fourier 1 Bulletin de la Société Mathématique de France 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Chinese Annals of Mathematics. Series B 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Japan Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Linear Algebra and its Applications 1 Journal of Dynamics and Differential Equations 1 Calculus of Variations and Partial Differential Equations 1 NoDEA. Nonlinear Differential Equations and Applications 1 Complexity 1 Differential Equations and Dynamical Systems 1 Regular and Chaotic Dynamics 1 Acta Mathematica Sinica. English Series 1 Annales Henri Poincaré 1 Physical Review E. Third Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Journal of Hyperbolic Differential Equations 1 Journal of Mathematical Physics, Analysis, Geometry 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Communications in Theoretical Physics 1 International Journal of Differential Equations 1 Science China. Mathematics 1 Symmetry 1 Advances in Nonlinear Analysis 1 Proceedings of the Royal Society of London. A. 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Mathematics & Physics ...and 2 more Serials all top 5 Cited in 35 Fields 383 Partial differential equations (35-XX) 186 Dynamical systems and ergodic theory (37-XX) 46 Fluid mechanics (76-XX) 40 Quantum theory (81-XX) 26 Ordinary differential equations (34-XX) 22 Statistical mechanics, structure of matter (82-XX) 19 Nonassociative rings and algebras (17-XX) 12 Differential geometry (53-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Mechanics of particles and systems (70-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Operator theory (47-XX) 8 Numerical analysis (65-XX) 6 Optics, electromagnetic theory (78-XX) 5 Difference and functional equations (39-XX) 5 Geophysics (86-XX) 5 Systems theory; control (93-XX) 4 Algebraic geometry (14-XX) 4 Real functions (26-XX) 4 Functional analysis (46-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-XX) 3 Integral equations (45-XX) 2 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Computer science (68-XX) Citations by Year