V. Gerdjikov

发表

Complete integrability of Nonlocal Nonlinear Schr\"odinger equation

V. Gerdjikov, A. Saxena, 2015, 1510.00480.

Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials.

V. Gerdjikov, B. Baizakov, M. Salerno, 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

Modeling Adiabatic N-Soliton Interactions and Perturbations

V. Gerdjikov, B. Baizakov, M. Salerno, 2004, cond-mat/0409741.

Inverse scattering transform for the Camassa–Holm equation

V. Gerdjikov, A. Constantin, R. Ivanov, 2006, Inverse Problems.

Two-dimensional Toda field equations related to the exceptional $\mathfrak{ g}_2$ algebra. Spectral properties of the Lax operators (Бойти)@@@Two-dimensional Toda field equations related to the exceptional algebra $\mathfrak g_2$: Spectral properties of the Lax operators

V. Gerdjikov, Владимир С Герджиков, 2012 .

The generalized Zakharov-Shabat system and the soliton perturbations

V. Gerdjikov, 1994 .

On the spectral theory of the integro-differential operator a generating nonlinear evolution equations

V. Gerdjikov, 1982 .

From generalized Fourier transforms to spectral curves for the Manakov hierarchy. I. Generalized Fourier transforms

A. O. Smirnov, V. Gerdjikov, V. Matveev, 2020, The European Physical Journal Plus.

Adiabatic interactions of Manakov solitons—Effects of cross-modulation

V. Gerdjikov, M. Todorov, A. Kyuldjiev, 2016, 1610.08413.

Real Hamiltonian forms of affine Toda field theories: spectral aspects

V. Gerdjikov, G. Grahovski, A. A. Stefanov, 2022, 2205.03844.

Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations

V. Gerdjikov, 1992 .

Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials.

V. Gerdjikov, B. Baizakov, M. Salerno, 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

Modeling Adiabatic N-Soliton Interactions and Perturbations

V. Gerdjikov, B. Baizakov, M. Salerno, 2004, cond-mat/0409741.

Manakov model with gain/loss terms and N-soliton interactions: Effects of periodic potentials

V. Gerdjikov, M. Todorov, 2018, Applied Numerical Mathematics.

N-soliton interactions: Effects of linear and nonlinear gain and loss

V. Gerdjikov, R. Carretero-González, M. Todorov, 2017 .

Fundamental analytic solutions for the Kulish-Sklyanin model with constant boundary conditions

A. O. Smirnov, V. Gerdjikov, 2021, AIP Conference Proceedings.

From generalized Fourier transforms to spectral curves for the Manakov hierarchy. II. Spectral curves for the Manakov hierarchy

A. O. Smirnov, V. Gerdjikov, V. Matveev, 2020 .

BREATHER SOLUTIONS OF A -WAVE EQUATIONS

V. Gerdjikov, T. Valchev, 2015 .

N-Wave Equations with Orthogonal Algebras: Z_2 and Z_2 \times Z_2 Reductions and Soliton Solutions

V. Gerdjikov, N. Kostov, T. Valchev, 2007, nlin/0703002.

RECURSION OPERATORS AND HIERARCHIES OF mKdV EQUATIONS RELATED TO THE KAC–MOODY ALGEBRAS D (1)4 , D (2)4 , AND D (3)4

V. Gerdjikov, V. Matveev, M. Pavlov, 2020 .

The complex Toda chains and the simple Lie algebras - solutions and large time asymptotics

Rossen I. Ivanov, Vladimir S. Gerdjikov, V. Gerdjikov, 1997, solv-int/9909020.

The Lax Representation and the AKNS Approach

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

The Classical r-Matrix Method

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

Algebraic and Analytic Aspects of Soliton Type Equations

Vladimir S. Gerdjikov, V. Gerdjikov, 2002, nlin/0206014.

Criterion and Regions of Stability for Quasi-Equidistant Soliton Trains.

Potsdam, V. Gerdjikov, G. Diankov, 1997, solv-int/9708004.

On Asymptotic Dynamical Regimes of Manakov N-soliton Trains in Adiabatic Approximation

V. Gerdjikov, M. Todorov, 2020, 2007.10959.

Polarization effects in modeling soliton interactions of the Manakov model

V. Gerdjikov, M. Todorov, A. Kyuldjiev, 2015 .

On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems

A. O. Smirnov, V. Gerdjikov, V. Matveev, 2021, Theoretical and Mathematical Physics.

Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems

Nikolay Kostov, V. S. Gerdjikov, Zoia Kostova, 1999, CASC.

On the Integrability of Ablowitz-Ladik models with local and nonlocal reductions

V. Gerdjikov, 2019, Journal of Physics: Conference Series.

On the soliton solutions of a family of Tzitzeica equations

V. Gerdjikov, C. N. Babalic, R. Constantinescu, 2017, 1703.05855.

The quadratic bundle of general form and the nonlinear evolution equations : expansions over the "squared" solutions - generalized Fourier transform

V. Gerdjikov, M. Ivanov, 1982 .

Basic Aspects of Soliton Theory

Vladimir S. Gerdjikov, V. Gerdjikov, 2006, nlin/0604004.

Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces

V. Gerdjikov, R. Ivanov, 2021, Nonlinearity.

On integrable wave interactions and Lax pairs on symmetric spaces

V. Gerdjikov, R. Ivanov, G. Grahovski, 2016, 1607.06940.

Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory

V. Gerdjikov, G. Grahovski, 2010, 1006.0301.

Solutions of multi-component NLS models and Spinor Bose–Einstein condensates

V. Gerdjikov, A. Kostov, T. Valchev, 2008, 0802.4398.

Integrable Hamiltonian Hierarchies

Gaetano Vilasi, Vladimir S. Gerdjikov, V. Gerdjikov, 2009 .

Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation

Vladimir S. Gerdjikov, V. Gerdjikov, 1986 .

Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type ?

V. Gerdjikov, N. Kostov, 2008, 0803.1651.

NONLINEAR SCHRODINGER EQUATION AND N-SOLITON INTERACTIONS : GENERALIZED KARPMAN-SOLOV'EV APPROACH AND THE COMPLEX TODA CHAIN

E. G. Evstatiev, Ivan M. Uzunov, Vladimir S. Gerdjikov, 1997 .

Real Hamiltonian forms of affine Toda field theories: Spectral aspects

V. Gerdjikov, G. Grahovski, A. A. Stefanov, 2022, Theoretical and Mathematical Physics.

Hierarchies of Hamiltonian structures

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

Fundamental Properties of the solvable NLEEs

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

The Inverse Scattering Problem for the Zakharov–Shabat System

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras

V. Gerdjikov, G. Grahovski, 2006, nlin/0602038.

ANALYTIC AND ALGEBRAIC ASPECTS OF TODA FIELD THEORIES AND THEIR REAL HAMILTONIAN FORMS

V. Gerdjikov, 2006 .

On Reductions and Real Hamiltonian Forms of Affine Toda Field Theories

V. Gerdjikov, G. Grahovski, 2005, nlin/0602042.

Real Hamiltonian forms of Hamiltonian systems

V. Gerdjikov, G. Marmo, G. Vilasi, 2003, nlin/0310005.

The complex Toda chains and the simple Lie algebras: II. Explicit solutions and asymptotic behaviour

Rossen I. Ivanov, Vladimir S. Gerdjikov, V. Gerdjikov, 2000 .

The N -Soliton Interactions, Complex Toda Chain and Stable Propagation of NLS Soliton Trains

V. Gerdjikov, G. Diankov, I. Uzunov, 1999 .

Stability and quasi-equidistant propagation of NLS soliton trains

E. G. Evstatiev, D. J. Kaup, Ivan M. Uzunov, 1998 .

Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces

V. Gerdjikov, A. Mikhailov, G. Grahovski, 2011, 1108.3990.

Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces

V. Gerdjikov, A. Mikhailov, T. Valchev, 2011 .

Reductions of integrable equations on A.III-type symmetric spaces

Vladimir S. Gerdjikov, V. Gerdjikov, Alexander V. Mikhailov, 2010, 1004.4182.

Riemann-Hilbert problem, integrability and reductions

V. Gerdjikov, R. Ivanov, A. Stefanov, 2019, Journal of Geometric Mechanics.

CBC Systems with Mikhailov Reductions by Coxeter Automorphism: I. Spectral Theory of the Recursion Operators

V. Gerdjikov, A. Yanovski, 2015 .

Integrable Hamiltonian Hierarchies: Spectral and Geometric Methods

Gaetano Vilasi, Vladimir S. Gerdjikov, V. Gerdjikov, 2008 .

Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system

V. Gerdjikov, A. Yanovski, 1994 .

Gauge covariant theory of the generating operator. I

V. Gerdjikov, A. Yanovski, 1986 .

Gauge covariant formulation of the generating operator. 2. Systems on homogeneous spaces

V. Gerdjikov, A. Yanovski, 1985 .

Gauge covariant formulation of the generating operator. 1. The Zakharov-Shabat system

V. Gerdjikov, A. Yanovski, 1984 .

Multisoliton interactions for the Manakov system under composite external potentials

V. Gerdjikov, M. Todorov, A. Kyuldjiev, 2015 .

Multicomponent Nonlinear Systems of Bose‐Fermi Fields: Exact Solutions

V. Gerdjikov, N. Kostov, T. Valchev, 2011 .

Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

N. A. Kostov, Vladimir S. Gerdjikov, V. Gerdjikov, 2007, nlin/0703057.

Two-component Bose-Einstein condensates in periodic potential.

V. Gerdjikov, V. Konotop, M. Salerno, 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

Exact solutions for a class of integrable HenonHeiles-type systems

V. Gerdjikov, N. Kostov, V. Mioc, 2009, 0911.4260.

On the Elliptic Null-Phase Solutions of the Kulish-Sklyanin Model

A. O. Smirnov, V. Gerdjikov, 2023, SSRN Electronic Journal.

Kulish–Sklyanin-type models: Integrability and reductions

V. Gerdjikov, 2017, Theoretical and Mathematical Physics.

On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms

V. Gerdjikov, 2017, 1703.03705.

Kulish–Sklyanin-type models: Integrability and reductions

V. Gerdjikov, 2017, 1702.04010.

Asymptotic behavior of Manakov solitons: Effects of potential wells and humps

V. S. Gerdjikov, M. D. Todorov, A. V. Kyuldjiev, 2014, Math. Comput. Simul..

Manakov solitons and effects of external potential wells

V. Gerdjikov, M. Todorov, A. Kyuldjiev, 2015 .

N -Soliton Interactions for the Manakov System: Effects of External Potentials

V. S. Gerdjikov, Michail D. Todorov, V. Gerdjikov, 2014 .

Bose-Einstein Condensates and Multi-Component NLS Models on Symmetric Spaces of BD.I-Type. Expansions over Squared Solutions

V. Gerdjikov, N. Kostov, D. Kaup, 2011 .

The Generalized Fourier Transforms

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

On Kaup-Kupershchmidt type equations and their soliton solutions

V. Gerdjikov, 2017, 1703.05850.

Riemann-Hilbert Problems, families of commuting operators and soliton equations

V. Gerdjikov, A. Yanovski, 2014 .

On Tzitzeica equation and spectral properties of related Lax operators

V. Gerdjikov, R. Constantinescu, N. Babalic, 2014 .

Two-dimensional Toda field equations related to the exceptional algebra $\mathfrak{g}_2 $: Spectral properties of the lax operators

V. Gerdjikov, 2012 .

The Direct Scattering Problem for theZakharov–Shabat System

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

Integrability and Nijenhuis Tensors

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

Soliton equations related to the affine Kac-Moody algebra D4(1)

V. Gerdjikov, A. A. Stefanov, S. Varbev, 2015, The European Physical Journal Plus.

Soliton equations related to the affine Kac-Moody algebra D4(1)

V. Gerdjikov, A. A. Stefanov, S. Varbev, 2014, 1412.2383.

REAL HAMILTONIAN FORMS FOR AFFINE TODA MODELS

V. Gerdjikov, G. Grahovski, 2006 .

The NLEEs and the Gauge Transformations

V. Gerdjikov, G. Vilasi, A. Yanovski, 2008 .

Gauge transformations and generating operators for the discrete Zakharov-Shabat system

V. Gerdjikov, M. Ivanov, Y. S. Yaklev, 1986 .

Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions

V. Gerdjikov, N. Kostov, V. S. Gerdjikov, 2005 .

On the multi‐component NLS type systems and their gauge equivalent: Examples and reductions

V. Gerdjikov, G. Grahovski, 2004 .

School of Mathematics 2006-0101 Inverse Scattering Transform for the Camassa-Holm equation

V. Gerdjikov, A. Constantin, R. Ivanov, 2019 .

Generalised Fourier transform for the Camassa-Holm hierarchy

V. Gerdjikov, A. Constantin, Rossen I Ivanov, 2007, 0707.2048.

S I ] 5 O ct 2 00 6 Inverse Scattering Transform for the Camassa-Holm equation

V. Gerdjikov, A. Constantin, R. Ivanov, 2006 .

S I ] 9 M ar 2 00 6 Inverse Scattering Transform for the Camassa-Holm equation

V. Gerdjikov, A. Constantin, R. Ivanov, 2006 .

The generating operator for the n × n linear system

Vladimir S. Gerdjikov, V. Gerdjikov, P. P. Kulish, 1981 .

On classification of soliton solutions of multicomponent nonlinear evolution equations

V. Gerdjikov, N. Kostov, D. Kaup, 2008 .

How Many Types of Soliton Solutions do We Know

David J. Kaup, Vladimir S. Gerdjikov, V. Gerdjikov, 2006 .

Recursion operators and the hierarchies of MKdV equations related to $D_4^{(1)}$, $D_4^{(2)}$ and $D_4^{(3)}$ Kac-Moody algebras

A. O. Smirnov, V. Gerdjikov, V. Matveev, 2020, 2006.16323.

The Manakov system as two moving interacting curves

V. Gerdjikov, N. Kostov, R. Dandoloff, 2007, 0707.0575.

Adiabatic interaction of N ultrashort solitons: universality of the complex Toda chain model.

V. Gerdjikov, J. Yang, J Yang, 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

Zakharov-Shabat System With Constant Boundary Conditions. Reflectionless Potentials and end Point Singularities

V. Gerdjikov, R. Ivanov, T. Valchev, 2014 .

From generalized Fourier transforms to spectral curves for the Manakov hierarchy. II. Spectral curves for the Manakov hierarchy

V. Gerdjikov, V. Matveev, A. Smirnov, 2020, The European Physical Journal Plus.

Superintegrability in the Manev Problem and its Real Form Dynamics

V. Gerdjikov, G. Marmo, G. Vilasi, 2006, nlin/0609002.

Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose-Einstein mixtures

Nikolay Kostov, V. S. Gerdjikov, E. V. Doktorov, 2009, Math. Comput. Simul..

On the 3-wave Equations with Constant Boundary Conditions

V. Gerdjikov, G. Grahovski, 2012, 1204.5346.

On Multicomponent mKDV Equations on Symmetric Spaces of DIII - Type and Their Reductions

V. Gerdjikov, N. Kostov, 2008 .

Expansions over the 'squared' solutions and the inhomogeneous nonlinear Schrodinger equation

V. Gerdjikov, M. Ivanov, 1992 .

Recursion operators and hierarchies of $$\text{mKdV}$$ equations related to the Kac–Moody algebras $$D_4^{(1)}$$, $$D_4^{(2)}$$, and $$D_4^{(3)}$$

A. O. Smirnov, V. Gerdjikov, V. Matveev, 2020 .

TWO SOLITON SOLUTION OF TZITZEICA EQUATION

V. Gerdjikov, C. N. Babalic, R. Constantinescu, 2013 .

Riemann-Hilbert Problems, Polynomial Lax Pairs, Integrable Equations and Their Soliton Solutions

V. Gerdjikov, A. A. Stefanov, 2023, Symmetry.

The N-wave equations with PT symmetry

V. Gerdjikov, R. Ivanov, G. Grahovski, 2016, 1601.01929.

How many types of soliton solutions do we know

T. I. Valchev, V. Gerdjikov, V. Kostov, 2007, 0708.1253.

N-wave interactions related to simple Lie algebras. ℤ2-reductions and soliton solutions

V. Gerdjikov, R. Ivanov, N. Kostov, 2000, nlin/0009034.

Reductions of N -wave interactions related to low-rank simple Lie algebras: I. Z2-reductions

V. Gerdjikov, N. Kostov, G. Grahovski, 2000, nlin/0006001.

$N$-Wave Type Systems and their Gauge Equivalent Related to the Orthogonal Algebras

V. Gerdjikov, N. Kostov, G. Grahovski, 2002 .

On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems

V. Gerdjikov, Nianhua Li, Vladimir B. Matveev, 2021, Theoretical and Mathematical Physics.

The Kulish-Sklyanin type hierarchy and spectral curves

E. E. Aman, V. Gerdjikov, A. Smirnov, 2021 .

Spectral curves for the multi-phase solutions of Manakov system

A. O. Smirnov, V. Gerdjikov, E. Frolov, 2020, IOP Conference Series: Materials Science and Engineering.

Two Soliton Interactions of BD.I Multicomponent NLS Equations and Their Gauge Equivalent

V. Gerdjikov, G. Grahovski, 2010 .

On reductions of soliton solutions of multi-component NLS models and spinor Bose-Einstein condensates

V. Gerdjikov, 2009, 1001.0166.

On the Spectral Properties of Lax Operators Related to BD.I Symmetric Spaces

V. Gerdjikov, A. Florian, Alina Streche-Pauna, 2021 .

Integrable Hamiltonian Hierarchies

V. Gerdjikov, G. Vilasi, A. Yanovski, 2009 .

On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources

V. Gerdjikov, R. Ivanov, G. Grahovski, 2011, 1109.4543.

01-01 On the ( Non )-Integrability of KdV Hierarchy with Self-consistent Sources

V. Gerdjikov, G. Grahovski, R. I. Ivanov, 2019 .

Generalised Fourier Transform for the Camassa-holm Hierarchy

V. Gerdjikov, Adrian Constantin, Rossen I. Ivanov, 2022 .

Multicomponent nonlinear Schrödinger equations with constant boundary conditions

V. Gerdjikov, N. Kostov, T. Valchev, 2009 .

N-Wave Equations with Orthogonal Algebras: Z 2 and Z 2 Z 2 Reduction

V. Gerdjikov, N. Kostov, T. Valchev, 2007 .