V. S. Gerdjikov, Gaetano Vilasi, Alexandar Yanovski, A. Yanovski

2013

In the past decades there has been significant progress in the theory of the nonlinear evolution equations that could be solved through some inverse scattering techniques (soliton equations orâ€¦ (More)

This is a review of two of the fundamental tools for analysis of soliton equations: i) the algebraic ones based on Kac-Moody algebras, their central extensions and their dual algebras which underlieâ€¦ (More)

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms ofâ€¦ (More)

The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem. We show how the secondâ€¦ (More)

We propose a compact and explicit expression for the solutions of the complex Toda chains related to the classical series of simple Lie algebras g. The solutions are parametrized by a minimal set ofâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2001

Using the Karpman-Solov'ev method we derive the equations for the two-soliton adiabatic interaction for solitons of the modified nonlinear SchrÃ¶dinger equation (MNSE). Then we generalize theseâ€¦ (More)

A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using theâ€¦ (More)

The reductions of the integrable N-wave type equations solvable by the inverse scattering method with the generalized Zakharov-Shabat systems L and related to some simple Lie algebra g are analyzed.â€¦ (More)

Abstract. The class of nonlinear evolution equations (NLEE) â€“ gauge equivalent to the N-wave equations related to the simple Lie algebra g are derived and analyzed. They are written in terms of S(x,â€¦ (More)