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Gerdzhikov, Vladimir Stefanov

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

98 Publications have been cited 892 times in 505 Documents Cited by Year
Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044
Constantin, 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 0522.35082
Gerdzhikov, V. S.; Ivanov, M. I.
49
1983
Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147
Gerdjikov, V. S.; Saxena, A.
48
2017
Integrable Hamiltonian hierarchies. Spectral and geometric methods. Zbl 1167.37001
Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov
43
2008
Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086
Gerdzhikov, V. S.
27
1986
The generating operator for the n \(\times n\) linear system. Zbl 1194.35365
Gerdjikov, V. S.; Kulish, P. P.
25
1981
Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system. Zbl 0814.34070
Gerdjikov, V. S.; Yanovski, A. B.
20
1994
The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090
Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I.
20
2016
Algebraic and analytic aspects of soliton type equations. Zbl 1026.37059
Gerdjikov, Vladimir S.
19
2002
Quadratic bundle and nonlinear equations. Zbl 0454.35071
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
18
1981
Solutions of multi-component NLS models and spinor Bose-Einstein condensates. Zbl 1167.82326
Gerdjikov, V. S.; Kostov, N. A.; Valchev, T. I.
17
2009
Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045
Constantin, 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 0988.35143
Gerdjikov, V. S.; Grahavoski, G. G.; Ivanov, R. I.; Kostov, N. A.
16
2001
Gauge covariant theory of the generating operator. I. Zbl 0611.35082
Gerdzhikov, 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 1001.37074
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
14
2001
Multicomponent NLS-type equations on symmetric spaces and their reductions. Zbl 1178.35347
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
13
2005
Expansions over the ”squared” solutions and difference evolution equations. Zbl 0554.35118
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
13
1984
Basic aspects of soliton theory. Zbl 1086.35102
Gerdjikov, Vladimir S.
11
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.
11
1998
On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180
Gerdjikov, 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 1248.37065
Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Mikhailov, Alexander V.; Valchev, Tihomir I.
10
2011
Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221
Gerdjikov, 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 1311.35247
Gerdjikov, V. S.; Yanovski, A. B.
8
2015
On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations. Zbl 0524.34029
Gerdzhikov, V. S.
8
1982
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.
8
2011
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.
7
2013
Quadratic bundle and nonlinear equations. Zbl 0439.35055
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
7
1980
\(N\)-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
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.
7
2004
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
7
2010
Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020
Gerdjikov, V. S.; Uzunov, I. M.
6
2001
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.
6
2008
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.
5
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.
5
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.
5
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
The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108
Gerdjikov, V. S.
5
1994
Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316
Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M.
5
2005
\(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129
Gerdjikov, V. S.
5
1990
Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053
Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A.
5
2019
Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326
Gerdjikov, V. S.
5
2017
Integrable Hamiltonian hierarchies. Spectral and geometric methods. Reprint of the 2008 hardback edition. Zbl 1293.37002
Gerdjikov, Vladimir Stefanov; Vilasi, Gaetano; Yanovski, Alexandar Borissov
4
2010
On multicomponent MKdV equations on symmetric spaces of DIII-type and their reductions. Zbl 1193.35184
Gerdjikov, 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 0522.35081
Gerdzhikov, V. S.; Ivanov, M. I.
4
1983
Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050
Gerdjikov, V. S.; Ivanov, M. I.
4
1992
Construction of real forms of complexified Hamiltonian dynamical systems. Zbl 1053.37031
Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G.
3
2003
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
Manakov solitons and effects of external potential wells. Zbl 1336.35325
Todorov, 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 0952.37048
Gerdjikov, V. S.; Evstatiev, E. G.; Ivanov, R. I.
3
2000
\(N\)-wave type systems and their gauge equivalent related to the orthogonal algebras. Zbl 1219.37051
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
3
2002
\(N\)-soliton interactions for the Manakov system: effects of external potentials. Zbl 1326.35343
Gerdjikov, V. S.; Todorov, M. D.
3
2014
The Manakov system as two moving interacting curves. Zbl 1142.35086
Kostov, 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 0522.35083
Gerdzhikov, V. S.; Kulish, P. P.
3
1983
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
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
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
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.
3
2006
Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. Zbl 0568.35084
Gerdzhikov, V. S.; Kulish, P. P.
3
1985
Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces. Zbl 1461.37071
Gerdjikov, Vladimir S.; Ivanov, Rossen I.
3
2021
Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194
Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V.
3
2017
Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions! Zbl 1053.37062
Gerdjikov, V. S.
2
2003
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
Lax representation does not mean complete integrability. Zbl 0941.35540
Gerdjikov, V. S.
2
1992
Exact solutions for a class of integrable Hénon-Heiles-type systems. Zbl 1309.70014
Kostov, N. A.; Gerdjikov, V. S.; Mioc, V.
2
2010
Breather solutions of \(N\)-wave equations. Zbl 1123.35342
Gerdjikov, 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 1134.37028
Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Valchev, Tihomir I.
2
2007
Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations. Zbl 0802.35137
Gerdjikov, V. S.
2
1992
On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522
Gerdjikov, V. S.; Grahovski, G. G.
2
2004
How many types of soliton solutions do we know? Zbl 1101.35069
Gerdjikov, 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 1456.37072
Gerdjikov, 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 1389.35290
Gerdjikov, 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 1218.37100
Gerdjikov, V. S.; Kaup, D. J.; Kostov, N. A.; Valchev, T. I.
2
2011
Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065
Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I.
2
2010
Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
2
2010
Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199
Gerdjikov, Vladimir S.
2
2011
The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 1510.37104
Gerdjikov, 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 1259.82127
Gerdjikov, Vladimir; Grahovski, Georgi; Mikhailov, Alexander; Valchev, Tihomir
2
2012
On the reductions and Hamiltonian structures of \(N\)-wave type equations. Zbl 1072.37050
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
1
2001
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
Real forms of complexified Hamiltonian dynamics. Zbl 1219.37043
Kyuldjiev, 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 1341.37038
Gerdjikov, V. S.
1
2012
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
Second order reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. Zbl 0999.35037
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
1
2000
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
Soliton equations with deep reductions. Generalized Fourier transforms. Zbl 1180.35444
Gerdjikov, V.; Kostov, N.; Valchev, T.
1
2007
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
Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type. Zbl 1157.37335
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
1
2008
On reductions and real Hamiltonian forms of affine Toda field theories. Zbl 1105.37041
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
1
2005
On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions. Zbl 1205.35292
Gerdjikov, Vladimir S.
1
2009
Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167
Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir
1
2010
Multi-component nonlinear Schrödinger equation on symmetric spaces with constant boundary conditions. I. Zbl 1203.37115
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
1
2010
Nonlinear evolution equations related to Kac-Moody algebras \(A_r^{(1)}\): spectral aspects. Zbl 1500.35258
Gerdjikov, Vladimir S.
1
2022
Riemann-Hilbert problems with canonical normalization and families of commuting operators. Zbl 07697254
Gerdjikov, V. S.
1
2012
On the 3-wave equations with constant boundary conditions. Zbl 07697255
Gerdjikov, V. S.; Grahovski, G. G.
1
2012
Nonlinear evolution equations related to Kac-Moody algebras \(A_r^{(1)}\): spectral aspects. Zbl 1500.35258
Gerdjikov, Vladimir S.
1
2022
Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces. Zbl 1461.37071
Gerdjikov, Vladimir S.; Ivanov, Rossen I.
3
2021
The mKdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac-Moody algebras. Zbl 1510.37104
Gerdjikov, 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 1456.37072
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.
5
2019
Complete integrability of nonlocal nonlinear Schrödinger equation. Zbl 1364.37147
Gerdjikov, V. S.; Saxena, A.
48
2017
On integrable wave interactions and Lax pairs on symmetric spaces. Zbl 1461.35180
Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Ivanov, Rossen I.
11
2017
Kulish-Sklyanin-type models: integrability and reductions. Zbl 1390.35326
Gerdjikov, V. S.
5
2017
Adiabatic interactions of Manakov solitons – effects of cross-modulation. Zbl 1461.35194
Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V.
3
2017
The \(N\)-wave equations with \(\mathcal{PT}\) symmetry. Zbl 1351.35090
Gerdjikov, V. S.; Grahovski, G. G.; Ivanov, R. I.
20
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.
8
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.
5
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.
5
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.
5
2015
Manakov solitons and effects of external potential wells. Zbl 1336.35325
Todorov, M. D.; Kyuldjiev, A. V.; Gerdjikov, V. S.
3
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
\(N\)-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.
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 1259.82127
Gerdjikov, 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 1341.37038
Gerdjikov, V. S.
1
2012
Riemann-Hilbert problems with canonical normalization and families of commuting operators. Zbl 07697254
Gerdjikov, V. S.
1
2012
On the 3-wave equations with constant boundary conditions. Zbl 07697255
Gerdjikov, V. S.; Grahovski, G. G.
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.
10
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.
8
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.
2
2011
Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Zbl 1210.35199
Gerdjikov, Vladimir S.
2
2011
Reductions of integrable equations on A.III-type symmetric spaces. Zbl 1202.35221
Gerdjikov, V. S.; Mikhailov, A. V.; Valchev, T. I.
9
2010
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory. Zbl 1218.37101
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
7
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
4
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
Recursion operators and reductions of integrable equations on symmetric spaces. Zbl 1217.37065
Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I.
2
2010
Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent. Zbl 1232.35142
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
2
2010
Differential resultant, computer algebra and completely integrable dynamical systems. Zbl 1202.65167
Kostova, Zoia; Kostov, Nikolay; Gerdjikov, Vladimir
1
2010
Multi-component nonlinear Schrödinger equation on symmetric spaces with constant boundary conditions. I. Zbl 1203.37115
Gerdjikov, Vladimir S.; Kostov, Nikolay A.
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.
17
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
43
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.
6
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
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.
17
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
Breather solutions of \(N\)-wave equations. Zbl 1123.35342
Gerdjikov, 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 1134.37028
Gerdjikov, Vladimir S.; Kostov, Nikolay A.; Valchev, Tihomir I.
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.
230
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.
3
2006
How many types of soliton solutions do we know? Zbl 1101.35069
Gerdjikov, Vladimir S.; Kaup, David J.
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.
13
2005
Basic aspects of soliton theory. Zbl 1086.35102
Gerdjikov, Vladimir S.
11
2005
Modeling adiabatic \(N\)-soliton interactions and perturbations. Zbl 1178.35316
Gerdjikov, V. S.; Baizakov, B. B.; Salerno, M.
5
2005
On the multi-component NLS type equations on symmetric spaces: reductions and soliton solutions. Zbl 1079.53075
Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A.
3
2005
On reductions and real Hamiltonian forms of affine Toda field theories. Zbl 1105.37041
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
1
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.
7
2004
On \(N\)-wave and NLS type systems: generating operator and gauge group action. Zbl 1100.35522
Gerdjikov, V. S.; Grahovski, G. G.
2
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
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.
19
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
Real forms of complexified Hamiltonian dynamics. Zbl 1219.37043
Kyuldjiev, 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 0988.35143
Gerdjikov, 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 1001.37074
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A.
14
2001
Adiabatic and non-adiabatic soliton interactions in nonlinear optics. Zbl 0972.78020
Gerdjikov, V. S.; Uzunov, I. M.
6
2001
On the reductions and Hamiltonian structures of \(N\)-wave type equations. Zbl 1072.37050
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
1
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.
3
2000
Second order reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. Zbl 0999.35037
Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay
1
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.
11
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.
20
1994
The generalized Zakharov-Shabat system and the soliton perturbations. Zbl 0850.35108
Gerdjikov, V. S.
5
1994
Expansions over the ‘squared’ solutions and the inhomogeneous nonlinear Schrödinger equation. Zbl 0766.35050
Gerdjikov, V. S.; Ivanov, M. I.
4
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.
2
1992
\(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. Zbl 0755.35129
Gerdjikov, V. S.
5
1990
Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation. Zbl 0603.35086
Gerdzhikov, V. S.
27
1986
Gauge covariant theory of the generating operator. I. Zbl 0611.35082
Gerdzhikov, V. S.; Yanovskij, A. B.
14
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.
13
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.
49
1983
The quadratic bundle of a general form and the nonlinear evolution equations. I: Expansions over the ”squared” solutions: generalized Fourier transform. Zbl 0522.35081
Gerdzhikov, V. S.; Ivanov, M. I.
4
1983
On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. Zbl 0522.35083
Gerdzhikov, V. S.; Kulish, P. P.
3
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.
25
1981
Quadratic bundle and nonlinear equations. Zbl 0454.35071
Gerdzhikov, V. S.; Ivanov, M. I.; Kulish, P. P.
18
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 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
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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. Theory, Methods & Applications. Series A: Theory and Methods
17 Physics Letters. A
16 Physica D
15 Wave Motion
15 Discrete and Continuous Dynamical Systems
13 Applicable Analysis
13 Communications in Mathematical Physics
13 Journal of Mathematical Analysis and Applications
12 Monatshefte für Mathematik
11 Applied Mathematics Letters
11 Nonlinear Dynamics
10 Journal of Geometry and Physics
9 Communications in Nonlinear Science and Numerical Simulation
9 Nonlinear Analysis. Real World Applications
7 Chaos, Solitons and Fractals
7 Journal of Physics A: Mathematical and Theoretical
6 Applied Mathematics and Computation
6 Studies in Applied Mathematics
6 Journal of Nonlinear Science
5 Letters in Mathematical Physics
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
5 Abstract and Applied Analysis
5 Journal of Mathematical Fluid Mechanics
5 Boundary Value Problems
5 Advances in Mathematical Physics
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Journal of Soviet Mathematics
4 Mathematical Physics, Analysis and Geometry
4 Ufimskiĭ Matematicheskiĭ Zhurnal
3 International Journal of Theoretical Physics
3 Reports on Mathematical Physics
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Journal of Computational and Applied Mathematics
3 Acta Applicandae Mathematicae
3 Chaos
3 Acta Mathematica Scientia. Series B. (English Edition)
3 International Journal of Geometric Methods in Modern Physics
3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
3 Communications in Theoretical Physics
2 Archive for Rational Mechanics and Analysis
2 Mathematical Methods in the Applied Sciences
2 Nonlinearity
2 Nuclear Physics. B
2 Advances in Mathematics
2 Journal of Functional Analysis
2 Quarterly of Applied Mathematics
2 Chinese Annals of Mathematics. Series B
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Applied Numerical Mathematics
2 Journal of Mathematical Sciences (New York)
2 Mathematical Problems in Engineering
2 Differential Equations
2 Journal of Evolution Equations
2 Discrete and Continuous Dynamical Systems. Series B
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 Advances in Difference Equations
2 Frontiers of Mathematics in China
2 International Journal of Applied and Computational Mathematics
2 Journal of Siberian Federal University. Mathematics & Physics
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 Advances in Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Japan Journal of Applied Mathematics
1 European 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 Turkish Journal of Mathematics
1 Fractals
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 Geometry and Symmetry in Physics
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
...and 9 more Serials

Citations by Year