V. S. Gerdjikov, G. Vilasi, A. B. Yanovski., Integrable Hamiltonian Hierarchies. Spectral and Geometric Methods, ISBN: 978-3-540-77054-1., Lecture Notes in Physics 748, 748, Springer Verlag, Berlin, Heidelberg, New York, 2008
V.S.Gerdjikov., “Generalised Fourier transforms for the soliton equations. Gauge covariant formulation.”, Inverse Problems, 2:1 (1986), 51-74
V S Gerdjikov, A B Yanovski., “CBC systems with Mikhailov reductions by Coxeter Automorphism. I. Spectral Theory of the Recursion Operators.”, DOI: 10.1111/sapm.12065., Studies in Applied Mathematics, 134:2 (2015), 145-180
V.S. Gerdjikov, A.O. Smirnov, V.B. Matveev,, “From generalized Fourier transforms to spectral curves for the Manakov hierarchy. I. Generalized Fourier transforms.”, 659, Eur. Phys. J. Plus, 135:8 (2020), 45
R.I. Ivanov and V. S. Gerdjikov., “Multicomponent Fokas-Lenells equa-tions on Hermitian symmetric spaces.”, Nonlinearity, 34 (2021), 939-963
V. S. Gerdjikov, Nianhua Li, V. B. Matveev, A. O. Smirnov, “On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems”, TMF, 213:1 (2022), 20–40; Theoret. and Math. Phys., 213:1 (2022), 1331–1347
V. S. Gerdjikov, G. G. Grahovski, A. A. Stefanov, “Real Hamiltonian forms of affine Toda field theories: Spectral aspects”, TMF, 212:2 (2022), 190–212; Theoret. and Math. Phys., 212:2 (2022), 1053–1072
2021
3.
V. S. Gerdjikov, D. M. Mladenov, A. A. Stefanov, S. K. Varbev, “The $\text{m}$KdV-type equations related to $A_5^{(1)}$ and $A_5^{(2)}$ Kac–Moody algebras”, TMF, 207:2 (2021), 237–260; Theoret. and Math. Phys., 207:2 (2021), 604–625
V. S. Gerdjikov, “On mKdV equations related to Kac-Moody algebras $A_5^{(1)}$ and $A_5^{(2)}$”, Ufimsk. Mat. Zh., 13:2 (2021), 121–140; Ufa Math. J., 13:2 (2021), 115–134
2020
5.
Vladimir S. Gerdjikov, Michail D. Todorov, “On asymptotic dynamical regimes of Manakov $N$-soliton trains in adiabatic approximation”, J. Sib. Fed. Univ. Math. Phys., 13:6 (2020), 678–693
6.
V. S. Gerdjikov, A. A. Stefanov, I. D. Iliev, G. P. Boyadjiev, A. O. Smirnov, V. B. Matveev, M. V. Pavlov, “Recursion operators and hierarchies of $\text{mKdV}$ equations related to the Kac–Moody algebras $D_4^{(1)}$, $D_4^{(2)}$, and $D_4^{(3)}$”, TMF, 204:3 (2020), 332–354; Theoret. and Math. Phys., 204:3 (2020), 1110–1129
V. S. Gerdjikov, “Kulish–Sklyanin-type models: Integrability and reductions”, TMF, 192:2 (2017), 187–206; Theoret. and Math. Phys., 192:2 (2017), 1097–1114
V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, “The $N$-wave equations with $\mathcal{PT}$ symmetry”, TMF, 188:3 (2016), 397–415; Theoret. and Math. Phys., 188:3 (2016), 1305–1321
V. S. Gerdjikov, “Two-dimensional Toda field equations related to the exceptional algebra $\mathfrak g_2$: Spectral properties of the Lax operators”, TMF, 172:2 (2012), 236–249; Theoret. and Math. Phys., 172:2 (2012), 1085–1096
Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov, Tihomir I. Valchev, “Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces”, SIGMA, 7 (2011), 096, 48 pp.
V. S. Gerdjikov, G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, “Rational bundles and recursion operators for integrable equations on A.III-type symmetric spaces”, TMF, 167:3 (2011), 394–406; Theoret. and Math. Phys., 167:3 (2011), 740–750
V. S. Gerdjikov, G. G. Grahovski, “Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory”, SIGMA, 6 (2010), 044, 29 pp.
V. S. Gerdjikov, N. A. Kostov, T. I. Valchev, “Multicomponent nonlinear schrödinger equations with constant
boundary conditions”, TMF, 159:3 (2009), 438–447; Theoret. and Math. Phys., 159:3 (2009), 787–795
Nikolay A. Kostov, Vladimir S. Gerdjikov, Tihomir I. Valchev, “Exact Solutions for Equations of Bose–Fermi Mixtures in One-Dimensional Optical Lattice”, SIGMA, 3 (2007), 071, 14 pp.
Vladimir S. Gerdjikov, Nikolay A. Kostov, Tihomir I. Valchev, “$N$-Wave Equations with Orthogonal Algebras: $\mathbb Z_2$ and $\mathbb Z_2\times\mathbb Z_2$ Reductions and Soliton Solutions”, SIGMA, 3 (2007), 039, 19 pp.
V. S. Gerdjikov, E. V. Doktorov, N. P. Matsuka, “$N$-soliton train and generalized complex Toda chain for the Manakov system”, TMF, 151:3 (2007), 391–404; Theoret. and Math. Phys., 151:3 (2007), 762–773
Vladimir S. Gerdjikov, Georgi G. Grahovski, “Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras”, SIGMA, 2 (2006), 022, 11 pp.
V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, “Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions”, TMF, 144:2 (2005), 313–323; Theoret. and Math. Phys., 144:2 (2005), 1147–1156
V. S. Gerdjikov, B. B. Baizakov, M. Salerno, “Modeling Adiabatic $N$-Soliton Interactions and Perturbations”, TMF, 144:2 (2005), 302–312; Theoret. and Math. Phys., 144:2 (2005), 1138–1146
V. S. Gerdjikov, “The generalized Zakharov–Shabat system and the soliton perturbations”, TMF, 99:2 (1994), 292–299; Theoret. and Math. Phys., 99:2 (1994), 593–598
V. S. Gerdjikov, P. P. Kulish, “On the multicomponent nonlinear Schrödinger equation in the case of non-vanishing boundary conditions”, Zap. Nauchn. Sem. LOMI, 131 (1983), 34–46
V. S. Gerdjikov, M. I. Ivanov, “Hamiltonian structure of multicomponent nonlinear Schrödinger equations in difference form”, TMF, 52:1 (1982), 89–104; Theoret. and Math. Phys., 52:1 (1982), 676–685
I. T. Gadzhiiev, V. S. Gerdjikov, M. I. Ivanov, “Hamiltonian structures for nonlinear evolution equations associated with polynomial bundles”, Zap. Nauchn. Sem. LOMI, 120 (1982), 55–68
V. S. Gerdjikov, P. P. Kulish, “Expansion in “square” eigenfunctions of matrix linear system”, Zap. Nauchn. Sem. LOMI, 101 (1981), 46–63; J. Soviet Math., 23:4 (1983), 2400–2412
V. S. Gerdjikov, E. Kh. Khristov, “Expansions in products of solutions of two Dirac systems”, Mat. Zametki, 28:4 (1980), 501–512; Math. Notes, 28:4 (1980), 710–716
V. S. Gerdjikov, M. I. Ivanov, P. P. Kulish, “Quadratic bundle and nonlinear equations”, TMF, 44:3 (1980), 342–357; Theoret. and Math. Phys., 44:3 (1980), 784–795
V. S. Gerdjikov, P. P. Kulish, “Derivation of the Bäcklund transformation in the formalism of the inverse scattering problem”, TMF, 39:1 (1979), 69–74; Theoret. and Math. Phys., 39:1 (1979), 327–331
V. S. Gerdjikov, P. P. Kulish, “Low-energy structure of the Feynman $S$-matrix”, TMF, 21:2 (1974), 183–194; Theoret. and Math. Phys., 21:2 (1974), 1065–1073
V. S. Gerdjikov, P. P. Kulish, “Low-energy for photons and infrared divergences”, TMF, 18:1 (1974), 51–55; Theoret. and Math. Phys., 18:1 (1974), 36–38
О полной интегрируемости двумеризованных полевых теорий Тода V. S. Gerdjikov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) April 4, 2018
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