A tail-matching method for the linear stability of multi-vector-soliton bound states

Abstract

Linear stability of multi-vector-soliton bound states in the coupled nonlinear Schrodinger equations is analyzed using a new tailmatching method. Under the condition that individual vector solitons in the bound states are wave-and-daughter-waves and widely separated, small eigenvalues of these bound states that bifurcate from the zero eigenvalue of single vector solitons are calculated explicitly. It is found that unstable eigenvalues from phase-mode bifurcations always exist, thus the bound states are always linearly unstable. This tail-matching method is simple, but it gives identical results as the Karpman-Solev'ev-Gorshkov-Ostrovsky method.Mathematics Subject Classification: 35Q55, 35Pxx, 74J35.

The new streamline diffusion for the 3D coupled Schrodinger equations with a cross-phase modulation

“…Yang [33] studied analytically the linear stability of twovector solitons bound states in the coupled nls equations by a tail-matching method. He obtained some conditions for small eigenvalues and he showed that these bound states are always linearly unstable due to the existence of one unstable phase-induced eigenvalue.…”

“…Also, the stability properties of such solutions for external perturbations as well as during interactions among themselves have been studied both numerically [20,23] and analytically [33]. For example, numerical simulations of the propagation and interactions of one-dimensional Langmuir solitons and their generation from random fluctuations by an external pump field were presented by Ismail and Taha [20,21,22,23,24].…”

“…Also, the coupled nonlinear Schrödinger equations (cnlse) is obtained in a great variety of physical situations [33,34]. For example, in fiber system, such equations have been shown to govern pulse propagation along orthogonal polarization axes [10,11,19,24,33,34].…”

“…For example, in fiber system, such equations have been shown to govern pulse propagation along orthogonal polarization axes [10,11,19,24,33,34]. Also, these equations model beam propagation inside photo or crystals refractives as well as water wave effects [33,34]. Solitary waves are called vector solitons as they generally contain two parts.…”

“…In addition to passing-through collision is an E53 important phenomena such that vector solitons also bounce off each other or trap each other. Solutions of this system have been studied intensively in recent years in numerical aspects and analytical [19,20,21,22,23,24,31,32,33,34,35,36,37]. Numerical examples were investigated by many authors in the one dimensional case [21,21,22,23,24,34].…”