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Gerdzhikov, Vladimir Stefanov

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Author ID: gerdzhikov.vladimir-stefanov Recent zbMATH articles by "Gerdzhikov, Vladimir Stefanov"
Published as: Gerdjikov, V. S.; Gerdjikov, Vladimir S.; Gerdjikov, Vladimir; Gerdzhikov, V. S.; Gerdjikov, Vladimir Stefanov; Gerdjikov, V.
Further Spellings: Gerjikov, Vladimir Stefanov
Homepage: http://www.inrne.bas.bg/index.php/scg/vladimir-gerdjikov
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Publications by Year

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 1105.37044
Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I.
212
2006
Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147
Gerdjikov, V. S.; Saxena, A.
37
2017
The quadratic bundle of general form and the nonlinear evolution equations. II: Hierarchies of structures. Zbl 0522.35082
Gerdzhikov, V. S.; Ivanov, M. I.
37
1983
Integrable Hamiltonian hierarchies. Spectral and geometric methods. Zbl 1167.37001
Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov
34
2008
The generating operator for the n \(\times n\) linear system. Zbl 1194.35365
Gerdjikov, V. S.; Kulish, P. P.
22
1981
Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086
Gerdzhikov, V. S.
21
1986
The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090
Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I.
18
2016
Quadratic bundle and nonlinear equations. Zbl 0454.35071
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
17
1981
Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045
Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I.
16
2007
Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system. Zbl 0814.34070
Gerdjikov, V. S.; Yanovski, A. B.
15
1994
\(N\)-wave interactions related to simple Lie algebras. \(\mathbb{Z}_2\)-reductions and soliton solutions. Zbl 0988.35143
Gerdjikov, V. S.; Grahavoski, G. G.; Ivanov, R. I.; Kostov, N. A.
15
2001
Algebraic and analytic aspects of soliton type equations. Zbl 1026.37059
Gerdjikov, Vladimir S.
14
2002
Reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. I: \(\mathbb Z_2\)-reductions. Zbl 1001.37074
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
12
2001
Expansions over the ”squared” solutions and difference evolution equations. Zbl 0554.35118
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
12
1984
Gauge covariant theory of the generating operator. I. Zbl 0611.35082
Gerdzhikov, V. S.; Yanovskij, A. B.
12
1986
Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326
Gerdjikov, V. S.; Kostov, N. A.; Valchev, T. I.
10
2009
Multicomponent NLS-type equations on symmetric spaces and their reductions. Zbl 1178.35347
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
10
2005
Stability and quasi-equidistant propagation of NLS soliton trains. Zbl 0948.81658
Gerdjikov, 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 1202.35221
Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I.
8
2010
Basic aspects of soliton theory. Zbl 1086.35102
Gerdjikov, Vladimir S.
8
2005
On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations. Zbl 0524.34029
Gerdzhikov, V. S.
8
1982
Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces. Zbl 1248.37065
Gerdjikov, 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 1142.37041
Gerdjikov, V. S.; Doktorov, E. V.; Matsuka, N. P.
7
2007
Quadratic bundle and nonlinear equations. Zbl 0439.35055
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
7
1980
On the \(N\)-wave equations and soliton interactions in two and three dimensions. Zbl 1365.35151
Gerdjikov, V. S.; Ivanov, R. I.; Kyuldjiev, A. V.
7
2011
Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020
Gerdjikov, V. S.; Uzunov, I. M.
6
2001
Two-component Bose-Einstein condensates in optical lattices. Zbl 1099.35529
Kostov, 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 1311.35247
Gerdjikov, V. S.; Yanovski, A. B.
6
2015
Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose-Einstein mixtures. Zbl 1251.35147
Gerdjikov, 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 0952.37049
Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I.
5
1998
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
5
2010
On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180
Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I.
5
2017
The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108
Gerdjikov, V. S.
4
1994
Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053
Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A.
4
2019
Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326
Gerdjikov, V. S.
4
2017
\(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129
Gerdjikov, V. S.
4
1990
On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
4
2008
On classification of soliton solutions of multicomponent nonlinear evolution equations. Zbl 1143.37048
Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I.
4
2008
Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316
Gerdjikov, 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 1293.35268
Gerdjikov, Vladimir S.; Yanovski, Alexandar B.
4
2013
\(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
3
2002
Construction of real forms of complexified Hamiltonian dynamical systems. Zbl 1053.37031
Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G.
3
2003
mKdV-type of equations related to \(B_2^{(1)}\) and \(A_4^{(2)}\). Zbl 1338.35392
Gerdjikov, 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 0618.35103
Gerdzhikov, V. S.; Ivanov, M. I.; Vaklev, Y. S.
3
1986
Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002
Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov
3
2010
Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. Zbl 0568.35084
Gerdzhikov, V. S.; Kulish, P. P.
3
1985
Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050
Gerdjikov, V. S.; Ivanov, M. I.
3
1992
Fordy-Kulish model and spinor Bose-Einstein condensate. Zbl 1163.82006
Atanasov, V. A.; Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
3
2008
The Manakov system as two moving interacting curves. Zbl 1142.35086
Kostov, 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 1139.82316
Kostov, 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 1079.53075
Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A.
3
2005
\(N\)-soliton interactions for the Manakov system: effects of external potentials. Zbl 1326.35343
Gerdjikov, V. S.; Todorov, M. D.
3
2014
Manakov solitons and effects of external potential wells. Zbl 1336.35325
Todorov, M. D.; Kyuldjiev, A. V.; Gerdjikov, V. S.
3
2015
Lax representation does not mean complete integrability. Zbl 0941.35540
Gerdjikov, V. S.
2
1992
The complex Toda chains and the simple Lie algebras. II: Explicit solutions and asymptotic behaviour. Zbl 0952.37048
Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I.
2
2000
Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions! Zbl 1053.37062
Gerdjikov, V. S.
2
2003
Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065
Gerdjikov, 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 1134.37028
Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Valchev, Tihomir I.
2
2007
Breather solutions of \(N\)-wave equations. Zbl 1123.35342
Gerdjikov, Vladimir; Valchev, Tihomir
2
2007
How many types of soliton solutions do we know? Zbl 1101.35069
Gerdjikov, 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 1101.35070
Grahovski, 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 1309.70014
Kostov, N. A.; Gerdjikov, V. S.; Mioc, V.
2
2010
Integrable equations and recursion operators related to the affine Lie algebras \(A_r^{(1)}\). Zbl 1317.35218
Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K.
2
2015
On the soliton solutions of a family of Tzitzeica equations. Zbl 1325.35188
Babalic, Corina N.; Constantinescu, Radu; Gerdjikov, Vladimir S.
2
2015
New types of two component NLS-type equations. Zbl 1389.35290
Gerdjikov, Vladimir; Stefanov, Aleksander
2
2016
Multisoliton interactions for the Manakov system under composite external potentials. Zbl 1330.35429
Todorov, Michail; Gerdjikov, Vladimir S.; Kyuldjiev, Assen V.
2
2015
On mKdV equations related to the affine Kac-Moody algebra \(A_5^{(2)}\). Zbl 1343.35208
Gerdjikov, 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 0522.35083
Gerdzhikov, 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 1456.37072
Gerdjikov, 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 0802.35137
Gerdjikov, V. S.
1
1992
The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 07364291
Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K.
1
2021
Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167
Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir
1
2010
Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199
Gerdjikov, Vladimir S.
1
2011
Bose-Einstein condensates and multi-component NLS models on symmetric spaces of BD. I-type. Expansions over squared solutions. Zbl 1218.37100
Gerdjikov, 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 1157.37335
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
1
2008
On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions. Zbl 1205.35292
Gerdjikov, 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 1259.82127
Gerdjikov, Vladimir; Grahovski, Georgi; Mikhailov, Alexander; Valchev, Tihomir
1
2012
Soliton equations with deep reductions. Generalized Fourier transforms. Zbl 1180.35444
Gerdjikov, V.; Kostov, N.; Valchev, T.
1
2007
On the multi-component NLS type systems and their gauge equivalent: examples and reductions. Zbl 1116.35355
Gerdjikov, V. S.; Grahovski, G. G.
1
2004
On the multi-component nonlinear Schrödinger equation with constant boundary conditions. Zbl 1120.81022
Atanasov, Victor; Gerdjikov, Vladimir
1
2006
Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil. Zbl 0597.35112
Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I.
1
1986
On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522
Gerdjikov, V. S.; Grahovski, G. G.
1
2004
On expansions in products of solutions of two Dirac systems. Zbl 0448.34025
Gerdzhikov, V. S.; Khristov, E. Kh.
1
1980
The expansion in ”square” of eigenfunctions of a matrix linear system. Zbl 0469.34015
Gerdzhikov, V. S.; Kulish, P. P.
1
1980
Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
1
2010
Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle. Zbl 0514.35078
Gadzhiev, 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 0522.35081
Gerdzhikov, V. S.; Ivanov, M. I.
1
1983
Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194
Gerdjikov, 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 07364291
Gerdjikov, 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 1456.37072
Gerdjikov, 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 1431.35053
Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A.
4
2019
Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147
Gerdjikov, V. S.; Saxena, A.
37
2017
On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180
Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I.
5
2017
Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326
Gerdjikov, V. S.
4
2017
Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194
Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V.
1
2017
The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090
Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I.
18
2016
New types of two component NLS-type equations. Zbl 1389.35290
Gerdjikov, Vladimir; Stefanov, Aleksander
2
2016
CBC systems with Mikhailov reductions by Coxeter automorphism. I: Spectral theory of the recursion operators. Zbl 1311.35247
Gerdjikov, V. S.; Yanovski, A. B.
6
2015
mKdV-type of equations related to \(B_2^{(1)}\) and \(A_4^{(2)}\). Zbl 1338.35392
Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K.
3
2015
Manakov solitons and effects of external potential wells. Zbl 1336.35325
Todorov, 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 1317.35218
Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K.
2
2015
On the soliton solutions of a family of Tzitzeica equations. Zbl 1325.35188
Babalic, Corina N.; Constantinescu, Radu; Gerdjikov, Vladimir S.
2
2015
Multisoliton interactions for the Manakov system under composite external potentials. Zbl 1330.35429
Todorov, Michail; Gerdjikov, Vladimir S.; Kyuldjiev, Assen V.
2
2015
On mKdV equations related to the affine Kac-Moody algebra \(A_5^{(2)}\). Zbl 1343.35208
Gerdjikov, 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 1326.35343
Gerdjikov, 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 1293.35268
Gerdjikov, 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 1259.82127
Gerdjikov, 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 1248.37065
Gerdjikov, 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 1365.35151
Gerdjikov, V. S.; Ivanov, R. I.; Kyuldjiev, A. V.
7
2011
Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199
Gerdjikov, Vladimir S.
1
2011
Bose-Einstein condensates and multi-component NLS models on symmetric spaces of BD. I-type. Expansions over squared solutions. Zbl 1218.37100
Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I.
1
2011
Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221
Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I.
8
2010
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
5
2010
Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002
Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov
3
2010
Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065
Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I.
2
2010
Exact solutions for a class of integrable Hénon-Heiles-type systems. Zbl 1309.70014
Kostov, N. A.; Gerdjikov, V. S.; Mioc, V.
2
2010
Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167
Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir
1
2010
Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
1
2010
Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326
Gerdjikov, 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 1251.35147
Gerdjikov, 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 1205.35292
Gerdjikov, Vladimir S.
1
2009
Integrable Hamiltonian hierarchies. Spectral and geometric methods. Zbl 1167.37001
Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov
34
2008
On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
4
2008
On classification of soliton solutions of multicomponent nonlinear evolution equations. Zbl 1143.37048
Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I.
4
2008
Fordy-Kulish model and spinor Bose-Einstein condensate. Zbl 1163.82006
Atanasov, 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 1157.37335
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
1
2008
Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045
Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I.
16
2007
\(N\)-soliton train and generalized complex Toda chain for the Manakov system. Zbl 1142.37041
Gerdjikov, V. S.; Doktorov, E. V.; Matsuka, N. P.
7
2007
The Manakov system as two moving interacting curves. Zbl 1142.35086
Kostov, 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 1139.82316
Kostov, 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 1134.37028
Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Valchev, Tihomir I.
2
2007
Breather solutions of \(N\)-wave equations. Zbl 1123.35342
Gerdjikov, Vladimir; Valchev, Tihomir
2
2007
Soliton equations with deep reductions. Generalized Fourier transforms. Zbl 1180.35444
Gerdjikov, V.; Kostov, N.; Valchev, T.
1
2007
Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044
Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I.
212
2006
How many types of soliton solutions do we know? Zbl 1101.35069
Gerdjikov, 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 1101.35070
Grahovski, 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 1120.81022
Atanasov, Victor; Gerdjikov, Vladimir
1
2006
Multicomponent NLS-type equations on symmetric spaces and their reductions. Zbl 1178.35347
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
10
2005
Basic aspects of soliton theory. Zbl 1086.35102
Gerdjikov, Vladimir S.
8
2005
Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316
Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M.
4
2005
On the multi-component NLS type equations on symmetric spaces: reductions and soliton solutions. Zbl 1079.53075
Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A.
3
2005
Two-component Bose-Einstein condensates in optical lattices. Zbl 1099.35529
Kostov, 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 1116.35355
Gerdjikov, V. S.; Grahovski, G. G.
1
2004
On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522
Gerdjikov, V. S.; Grahovski, G. G.
1
2004
Construction of real forms of complexified Hamiltonian dynamical systems. Zbl 1053.37031
Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G.
3
2003
Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions! Zbl 1053.37062
Gerdjikov, V. S.
2
2003
Algebraic and analytic aspects of soliton type equations. Zbl 1026.37059
Gerdjikov, Vladimir S.
14
2002
\(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
3
2002
\(N\)-wave interactions related to simple Lie algebras. \(\mathbb{Z}_2\)-reductions and soliton solutions. Zbl 0988.35143
Gerdjikov, 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 1001.37074
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
12
2001
Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020
Gerdjikov, V. S.; Uzunov, I. M.
6
2001
The complex Toda chains and the simple Lie algebras. II: Explicit solutions and asymptotic behaviour. Zbl 0952.37048
Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I.
2
2000
Stability and quasi-equidistant propagation of NLS soliton trains. Zbl 0948.81658
Gerdjikov, 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 0952.37049
Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I.
5
1998
Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system. Zbl 0814.34070
Gerdjikov, V. S.; Yanovski, A. B.
15
1994
The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108
Gerdjikov, V. S.
4
1994
Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050
Gerdjikov, V. S.; Ivanov, M. I.
3
1992
Lax representation does not mean complete integrability. Zbl 0941.35540
Gerdjikov, V. S.
2
1992
Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations. Zbl 0802.35137
Gerdjikov, V. S.
1
1992
\(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129
Gerdjikov, V. S.
4
1990
Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086
Gerdzhikov, V. S.
21
1986
Gauge covariant theory of the generating operator. I. Zbl 0611.35082
Gerdzhikov, V. S.; Yanovskij, A. B.
12
1986
Gauge transformations and generating operators for the discrete Zakharov- Shabat system. Zbl 0618.35103
Gerdzhikov, V. S.; Ivanov, M. I.; Vaklev, Y. S.
3
1986
Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil. Zbl 0597.35112
Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I.
1
1986
Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. Zbl 0568.35084
Gerdzhikov, V. S.; Kulish, P. P.
3
1985
Expansions over the ”squared” solutions and difference evolution equations. Zbl 0554.35118
Gerdzhikov, 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 0522.35082
Gerdzhikov, V. S.; Ivanov, M. I.
37
1983
On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. Zbl 0522.35083
Gerdzhikov, 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 0522.35081
Gerdzhikov, V. S.; Ivanov, M. I.
1
1983
On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations. Zbl 0524.34029
Gerdzhikov, V. S.
8
1982
Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle. Zbl 0514.35078
Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I.
1
1982
The generating operator for the n \(\times n\) linear system. Zbl 1194.35365
Gerdjikov, V. S.; Kulish, P. P.
22
1981
Quadratic bundle and nonlinear equations. Zbl 0454.35071
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
17
1981
Quadratic bundle and nonlinear equations. Zbl 0439.35055
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
7
1980
On expansions in products of solutions of two Dirac systems. Zbl 0448.34025
Gerdzhikov, V. S.; Khristov, E. Kh.
1
1980
The expansion in ”square” of eigenfunctions of a matrix linear system. Zbl 0469.34015
Gerdzhikov, V. S.; Kulish, P. P.
1
1980
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. Mathematical, Physical and Engineering Sciences
1 Journal of Siberian Federal University. Mathematics & Physics
...and 2 more Serials

Citations by Year