381 citations · 1.1k across the 65 of their papers we have counts for
66 papers
On the -waves hierarchy with constant boundary conditions. Spectral properties
Vladimir S. Gerdjikov, Georgi G. Grahovski
The paper is devoted to -wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators , w…
On affine Toda field theories related to algebras and their real Hamiltonian forms
Vladimir S. Gerdjikov, Georgi G. Grahovski
The paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series . We demonstrate that the complexification procedure…
Real Hamiltonian forms of affine Toda field theories: spectral aspects
Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander A. Stefanov
The paper is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax ope…
Fundamental Analytic Solutions for the Kulish-Sklyanin Model with Constant Boundary Conditions
Vladimir S. Gerdjikov, Aleksandr O. Smirnov
In the present paper we analyze the construction of fundamental analytic solutions (FAS) for the generalized Kulish-Sklyanin models (KSM) for vanishing (VBC) and constant boundary…
On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems
Vladimir S. Gerdjikov, Nianhua Li, Vladimir B. Matveev +1
In this paper we consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota-Ohta system. The Lax pair of the Hirota-Ohta system was extended to a Lax…
On the mKdV equations related to the Kac-Moody algebras and
Vladimir S. Gerdjikov
We outline the derivation of the mKdV equations related to the Kac-Moody algebras and . First we formulate their Lax representations and provide details how…