Edit Profile (opens in new tab) Gerdzhikov, Vladimir Stefanov Co-Author Distance 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: 133 Publications since 1980, including 2 Books 2 Contributions as Editor Co-Authors: 50 Co-Authors with 113 Joint Publications 842 Co-Co-Authors all top 5 Co-Authors 21 single-authored 30 Kostov, Nikolay A. 23 Grahovski, Georgi G. 16 Valchev, Tihomir I. 12 Ivanov, Rossen I. 11 Kyuldjiev, Assen V. 9 Ivanov, Maksim I. 9 Stefanov, Aleksander A. 8 Kulish, Petr Petrovich 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. 3 Matveev, Vladimir B. 3 Smirnov, Alexander O. 2 Constantin, Adrian 2 Constantinescu, Radu D. 2 Doktorov, Evgeny V. 2 Gadzhiev, I. T. 2 Khristov, Evgeni Khristov 2 Matsuka, N. P. 2 Pavlov, Maxim V. 2 Salerno, Mario 2 Sekigawa, Kouei 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 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 Li, Nianhua 1 Matsushita, Yasuo 1 Mioc, Vasile 1 Mladenov, Ivaĭlo M. 1 Vaklev, Y. S. 1 Yanovskij, A. B. all top 5 Serials 14 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 PLISKA. Studia Mathematica Bulgarica 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 Turkish Journal of 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 107 Partial differential equations (35-XX) 92 Dynamical systems and ergodic theory (37-XX) 21 Quantum theory (81-XX) 19 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 Potential theory (31-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 98 Publications have been cited 892 times in 505 Documents Cited by ▼ Year ▼ Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I. 230 2006 The quadratic bundle of general form and the nonlinear evolution equations. II: Hierarchies of structures. Zbl 0522.35082Gerdzhikov, V. S.; Ivanov, M. I. 49 1983 Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147Gerdjikov, V. S.; Saxena, A. 48 2017 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Zbl 1167.37001Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 43 2008 Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086Gerdzhikov, V. S. 27 1986 The generating operator for the n \(\times n\) linear system. Zbl 1194.35365Gerdjikov, V. S.; Kulish, P. P. 25 1981 Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system. Zbl 0814.34070Gerdjikov, V. S.; Yanovski, A. B. 20 1994 The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I. 20 2016 Algebraic and analytic aspects of soliton type equations. Zbl 1026.37059Gerdjikov, Vladimir S. 19 2002 Quadratic bundle and nonlinear equations. Zbl 0454.35071Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 18 1981 Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326Gerdjikov, V. S.; Kostov, N. A.; Valchev, T. I. 17 2009 Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I. 17 2007 \(N\)-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. 16 2001 Gauge covariant theory of the generating operator. I. Zbl 0611.35082Gerdzhikov, V. S.; Yanovskij, A. B. 14 1986 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. 14 2001 Multicomponent NLS-type equations on symmetric spaces and their reductions. Zbl 1178.35347Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 13 2005 Expansions over the ”squared” solutions and difference evolution equations. Zbl 0554.35118Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 13 1984 Basic aspects of soliton theory. Zbl 1086.35102Gerdjikov, Vladimir S. 11 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. 11 1998 On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I. 11 2017 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. 10 2011 Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I. 9 2010 CBC systems with Mikhailov reductions by Coxeter automorphism. I: Spectral theory of the recursion operators. Zbl 1311.35247Gerdjikov, V. S.; Yanovski, A. B. 8 2015 On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations. Zbl 0524.34029Gerdzhikov, V. S. 8 1982 On the \(N\)-wave equations and soliton interactions in two and three dimensions. Zbl 1365.35151Gerdjikov, V. S.; Ivanov, R. I.; Kyuldjiev, A. V. 8 2011 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. 7 2013 Quadratic bundle and nonlinear equations. Zbl 0439.35055Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 7 1980 \(N\)-soliton train and generalized complex Toda chain for the Manakov system. Zbl 1142.37041Gerdjikov, V. S.; Doktorov, E. V.; Matsuka, N. P. 7 2007 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. 7 2004 Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101Gerdjikov, Vladimir S.; Grahovski, Georgi G. 7 2010 Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020Gerdjikov, V. S.; Uzunov, I. M. 6 2001 On classification of soliton solutions of multicomponent nonlinear evolution equations. Zbl 1143.37048Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I. 6 2008 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. 5 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. 5 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. 5 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 The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108Gerdjikov, V. S. 5 1994 Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M. 5 2005 \(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129Gerdjikov, V. S. 5 1990 Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A. 5 2019 Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326Gerdjikov, V. S. 5 2017 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 4 2010 On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184Gerdjikov, Vladimir S.; Kostov, Nikolay A. 4 2008 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. 4 1983 Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050Gerdjikov, V. S.; Ivanov, M. I. 4 1992 Construction of real forms of complexified Hamiltonian dynamical systems. Zbl 1053.37031Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G. 3 2003 Gauge transformations and generating operators for the discrete Zakharov- Shabat system. Zbl 0618.35103Gerdzhikov, V. S.; Ivanov, M. I.; Vaklev, Y. S. 3 1986 Manakov solitons and effects of external potential wells. Zbl 1336.35325Todorov, M. D.; Kyuldjiev, A. V.; Gerdjikov, V. S. 3 2015 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. 3 2000 \(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 3 2002 \(N\)-soliton interactions for the Manakov system: effects of external potentials. Zbl 1326.35343Gerdjikov, V. S.; Todorov, M. D. 3 2014 The Manakov system as two moving interacting curves. Zbl 1142.35086Kostov, N. A.; Dandoloff, R.; Gerdjikov, V. S.; Grahovski, G. G. 3 2007 On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. Zbl 0522.35083Gerdzhikov, V. S.; Kulish, P. P. 3 1983 Fordy-Kulish model and spinor Bose-Einstein condensate. Zbl 1163.82006Atanasov, V. A.; Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. 3 2008 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 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 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. 3 2006 Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. Zbl 0568.35084Gerdzhikov, V. S.; Kulish, P. P. 3 1985 Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces. Zbl 1461.37071Gerdjikov, Vladimir S.; Ivanov, Rossen I. 3 2021 Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V. 3 2017 Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions! Zbl 1053.37062Gerdjikov, V. S. 2 2003 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 Lax representation does not mean complete integrability. Zbl 0941.35540Gerdjikov, V. S. 2 1992 Exact solutions for a class of integrable Hénon-Heiles-type systems. Zbl 1309.70014Kostov, N. A.; Gerdjikov, V. S.; Mioc, V. 2 2010 Breather solutions of \(N\)-wave equations. Zbl 1123.35342Gerdjikov, Vladimir; Valchev, Tihomir 2 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 Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations. Zbl 0802.35137Gerdjikov, V. S. 2 1992 On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522Gerdjikov, V. S.; Grahovski, G. G. 2 2004 How many types of soliton solutions do we know? Zbl 1101.35069Gerdjikov, Vladimir S.; Kaup, David J. 2 2006 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 New types of two component NLS-type equations. Zbl 1389.35290Gerdjikov, Vladimir; Stefanov, Aleksander 2 2016 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. 2 2011 Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I. 2 2010 Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142Gerdjikov, Vladimir S.; Grahovski, Georgi G. 2 2010 Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199Gerdjikov, Vladimir S. 2 2011 The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 1510.37104Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 2 2021 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 2 2012 On the reductions and Hamiltonian structures of \(N\)-wave type equations. Zbl 1072.37050Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 1 2001 Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil. Zbl 0597.35112Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. 1 1986 Real forms of complexified Hamiltonian dynamics. Zbl 1219.37043Kyuldjiev, Assen; Gerdjikov, Vladimir; Marmo, Giuseppe; Vilasi, Gaetano 1 2002 Two-dimensional Toda field equations related to the exceptional algebra \(\mathfrak g_2\): spectral properties of the Lax operators. Zbl 1341.37038Gerdjikov, V. S. 1 2012 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 Second order reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. Zbl 0999.35037Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 1 2000 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 Soliton equations with deep reductions. Generalized Fourier transforms. Zbl 1180.35444Gerdjikov, V.; Kostov, N.; Valchev, T. 1 2007 Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle. Zbl 0514.35078Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. 1 1982 Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type. Zbl 1157.37335Gerdjikov, Vladimir S.; Kostov, Nikolay A. 1 2008 On reductions and real Hamiltonian forms of affine Toda field theories. Zbl 1105.37041Gerdjikov, Vladimir S.; Grahovski, Georgi G. 1 2005 On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions. Zbl 1205.35292Gerdjikov, Vladimir S. 1 2009 Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir 1 2010 Multi-component nonlinear Schrödinger equation on symmetric spaces with constant boundary conditions. I. Zbl 1203.37115Gerdjikov, Vladimir S.; Kostov, Nikolay A. 1 2010 Nonlinear evolution equations related to Kac-Moody algebras \(A_r^{(1)}\): spectral aspects. Zbl 1500.35258Gerdjikov, Vladimir S. 1 2022 Riemann-Hilbert problems with canonical normalization and families of commuting operators. Zbl 07697254Gerdjikov, V. S. 1 2012 On the 3-wave equations with constant boundary conditions. Zbl 07697255Gerdjikov, V. S.; Grahovski, G. G. 1 2012 Nonlinear evolution equations related to Kac-Moody algebras \(A_r^{(1)}\): spectral aspects. Zbl 1500.35258Gerdjikov, Vladimir S. 1 2022 Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces. Zbl 1461.37071Gerdjikov, Vladimir S.; Ivanov, Rossen I. 3 2021 The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 1510.37104Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K. 2 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. 5 2019 Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147Gerdjikov, V. S.; Saxena, A. 48 2017 On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I. 11 2017 Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326Gerdjikov, V. S. 5 2017 Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V. 3 2017 The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I. 20 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. 8 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. 5 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. 5 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. 5 2015 Manakov solitons and effects of external potential wells. Zbl 1336.35325Todorov, M. D.; Kyuldjiev, A. V.; Gerdjikov, V. S. 3 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 \(N\)-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. 7 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 2 2012 Two-dimensional Toda field equations related to the exceptional algebra \(\mathfrak g_2\): spectral properties of the Lax operators. Zbl 1341.37038Gerdjikov, V. S. 1 2012 Riemann-Hilbert problems with canonical normalization and families of commuting operators. Zbl 07697254Gerdjikov, V. S. 1 2012 On the 3-wave equations with constant boundary conditions. Zbl 07697255Gerdjikov, V. S.; Grahovski, G. G. 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. 10 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. 8 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. 2 2011 Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199Gerdjikov, Vladimir S. 2 2011 Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I. 9 2010 Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101Gerdjikov, Vladimir S.; Grahovski, Georgi G. 7 2010 Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov 4 2010 Exact solutions for a class of integrable Hénon-Heiles-type systems. Zbl 1309.70014Kostov, N. A.; Gerdjikov, V. S.; Mioc, V. 2 2010 Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I. 2 2010 Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142Gerdjikov, Vladimir S.; Grahovski, Georgi G. 2 2010 Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir 1 2010 Multi-component nonlinear Schrödinger equation on symmetric spaces with constant boundary conditions. I. Zbl 1203.37115Gerdjikov, Vladimir S.; Kostov, Nikolay A. 1 2010 Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326Gerdjikov, V. S.; Kostov, N. A.; Valchev, T. I. 17 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 43 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. 6 2008 On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184Gerdjikov, Vladimir S.; Kostov, Nikolay A. 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. 17 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 Breather solutions of \(N\)-wave equations. Zbl 1123.35342Gerdjikov, Vladimir; Valchev, Tihomir 2 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 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. 230 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. 3 2006 How many types of soliton solutions do we know? Zbl 1101.35069Gerdjikov, Vladimir S.; Kaup, David J. 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. 13 2005 Basic aspects of soliton theory. Zbl 1086.35102Gerdjikov, Vladimir S. 11 2005 Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M. 5 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 On reductions and real Hamiltonian forms of affine Toda field theories. Zbl 1105.37041Gerdjikov, Vladimir S.; Grahovski, Georgi G. 1 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. 7 2004 On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522Gerdjikov, V. S.; Grahovski, G. G. 2 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 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. 19 2002 \(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 3 2002 Real forms of complexified Hamiltonian dynamics. Zbl 1219.37043Kyuldjiev, Assen; Gerdjikov, Vladimir; Marmo, Giuseppe; Vilasi, Gaetano 1 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. 16 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. 14 2001 Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020Gerdjikov, V. S.; Uzunov, I. M. 6 2001 On the reductions and Hamiltonian structures of \(N\)-wave type equations. Zbl 1072.37050Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 1 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. 3 2000 Second order reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. Zbl 0999.35037Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay 1 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. 11 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. 20 1994 The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108Gerdjikov, V. S. 5 1994 Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050Gerdjikov, V. S.; Ivanov, M. I. 4 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. 2 1992 \(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129Gerdjikov, V. S. 5 1990 Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086Gerdzhikov, V. S. 27 1986 Gauge covariant theory of the generating operator. I. Zbl 0611.35082Gerdzhikov, V. S.; Yanovskij, A. B. 14 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. 13 1984 The quadratic bundle of general form and the nonlinear evolution equations. II: Hierarchies of structures. Zbl 0522.35082Gerdzhikov, V. S.; Ivanov, M. I. 49 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. 4 1983 On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. Zbl 0522.35083Gerdzhikov, V. S.; Kulish, P. P. 3 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. 25 1981 Quadratic bundle and nonlinear equations. Zbl 0454.35071Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P. 18 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 564 Authors 38 Gerdzhikov, Vladimir Stefanov 22 Yin, Zhaoyang 21 Mi, Yongsheng 18 Mu, Chunlai 16 Zhou, Shouming 14 Guo, Boling 14 Ma, Wen-Xiu 13 Ivanov, Rossen I. 12 Liu, Yue 12 Qiao, Zhijun 10 Gürses, Metin 9 Grahovski, Georgi G. 9 Pekcan, Asli 9 Qu, Changzheng 8 Fan, Engui 8 Guo, Yingying 8 Shepelsky, Dmitry 8 Tian, Lixin 7 Chen, Yong 7 Kostov, Nikolay A. 7 Shen, Chunyu 7 Valchev, Tihomir I. 7 Yan, Zhenya 7 Yang, Bo 6 Li, Nianhua 5 Boutet de Monvel, Anne Marie 5 Gao, Anna 5 Geng, Xianguo 5 Lai, Shaoyong 5 Prinari, Barbara 5 Qiu, Deqin 5 Sakhnovich, Alexander L. 5 Stefanov, Aleksander A. 5 Todorov, Michail D. 5 Zheng, Rudong 5 Zhu, Mingxuan 4 Constantin, Adrian 4 Fokas, Athanassios S. 4 Guo, Zhengguang 4 Huang, Daiwen 4 Liu, Xiaochuan 4 Liu, Zhengrong 4 Luo, Ting 4 Matveev, Vladimir B. 4 Moon, Byungsoo 4 Myrzakulov, Ratbay 4 Smirnov, Alexander O. 4 Xia, Baoqiang 4 Yang, Jianke 4 Yang, Shaojie 4 Ye, Weikui 4 Zhang, Guoqiang 4 Zhang, Lei 4 Zhang, Ling 3 Chen, Jinbing 3 Chen, Rong 3 Chow, Kwok Wing 3 Christov, Ognyan 3 Doungmo Goufo, Emile Franc 3 Duruk Mutlubaş, Nilay 3 Fu, Ying 3 Geyer, Anna 3 Guan, Chunxia 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 Li, Hongmin 3 Lv, Cong 3 Mladenov, Dimitar M. 3 Mukherjee, Indranil 3 Mustafa, Octavian G. 3 Olver, Peter John 3 Qin, Guoquan 3 Rybalko, Yan 3 Senthilvelan, Murugaian 3 Tian, Shoufu 3 Varbev, Stanislav K. 3 Wang, Ying 3 Xu, Jian 3 Xue, Bo 3 Yang, Li 3 Zhang, Baoshuai 3 Zhang, Yi 3 Zhu, Min 2 Ablowitz, Mark Jay 2 Arnaudon, Alexis 2 Belmonte-Beitia, Juan 2 Bogolyubov, Nikolaĭ Mikhaĭlovich 2 Carroll, Robert Wayne 2 Cheng, Wenguang 2 Cheng, Yi 2 Chung, Won-Sang ...and 464 more Authors all top 5 Cited in 109 Serials 38 Journal of Mathematical Physics 33 Theoretical and Mathematical Physics 27 Journal of Nonlinear Mathematical Physics 25 Journal of Differential Equations 18 Nonlinear Analysis. 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Series S 1 Kinetic and Related Models ...and 9 more Serials all top 5 Cited in 35 Fields 445 Partial differential equations (35-XX) 231 Dynamical systems and ergodic theory (37-XX) 53 Fluid mechanics (76-XX) 43 Quantum theory (81-XX) 26 Ordinary differential equations (34-XX) 23 Nonassociative rings and algebras (17-XX) 22 Statistical mechanics, structure of matter (82-XX) 14 Differential geometry (53-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Numerical analysis (65-XX) 10 Mechanics of particles and systems (70-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Operator theory (47-XX) 7 Algebraic geometry (14-XX) 6 Difference and functional equations (39-XX) 6 Optics, electromagnetic theory (78-XX) 5 Real functions (26-XX) 5 Integral equations (45-XX) 5 Geophysics (86-XX) 5 Systems theory; control (93-XX) 4 Functional analysis (46-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-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 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Combinatorics (05-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 Probability theory and stochastic processes (60-XX) Citations by Year