We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity–free perturbation theory, we show that the well known N–soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N–soliton solution that satisfies si...

We describe an iterative method that extracts the underlying soliton from a noisy pulse. The method is formulated as a functional iteration: at each step, the soliton component of the difference between the noisy pulse and the current underlying soliton is determined via soliton perturbation theory; this is then added to the soliton, and the process is repeated. We show that this iteration conv...

The adiabatic parameter dynamics of solitons due to Gardner’s equation is obtained, in presence of the perturbation terms, by the aid of soliton perturbation theory. In addition, the integrals of motion are evaluated as well as the variation of the velocity is obtained due to these perturbation terms. Mathematics Subject Classification: 35Q51, 35Q53, 37K10 PACS Codes: 02.30.Jr, 02.30.Ik 788 A. ...

Propagation of incoherently soliton pairs in photorefractive crystals under steady-state conditions is studied. These soliton states can be generated when the two mutually incoherent optical beams with the same polarization and wavelength incident on the biased photorefractive crystal. Such soliton pairs can exist in bright-bright, dark-dark, gray-gray as well as in bright-dark types. In this p...

Complete eigenfunctions of linearized integrable equations expanded around an arbitrary solution are obtained for the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and the Korteweg-de Vries (KdV) hierarchy. It is shown that the linearization operators and the recursion operator which generates the hierarchy are commutable. Consequently, eigenfunctions of the linearization operators are precisely ...

We study the quantum conserved charges and S-matrices of N=2 supersymmetric sine-Gordon theory in the framework of perturbation theory formulated in N=2 superspace. The quantum affine algebras ̂ slq(2) and super topological charges play important roles in determining the N=2 soliton structure and S-matrices of soliton-(anti)soliton as well as soliton-breather scattering. ∗Presented by T. Uematsu...

This paper presents the perturbation theory for the double–sine–Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation’s influence. In particular case λ = 0 the results of the research transform into well-known perturbation theory for the sine–Gordon equation.

: Optical separate spatial dark and bright soliton pairs in steady-state case in one dimension, for a series circuit consisting of two-photon photorefractive (PR) crystal are investigated. Each crystal can be supported the spatial soliton, and at least one must be photovoltaic. The two solitons are known collectively as separate spatial soliton pairs with dark–dark, bright–dark and bright–brigh...

: optical separate spatial dark and bright soliton pairs in steady-state case in one dimension, for a series circuit consisting of two-photon photorefractive (pr) crystal are investigated. each crystal can be supported the spatial soliton, and at least one must be photovoltaic. the two solitons are known collectively as separate spatial soliton pairs with dark–dark, bright–dark and bright–brigh...