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We numerically study solitary waves in the coupled nonlinear Schrodinger equations. We detect pitchfork bifurcations of the fundamental solitary wave and compute eigenvalues and eigenfunctions of the corresponding eigenvalue problems to determine the spectral stability of solitary waves born at the pitchfork bifurcations. Our numerical results demonstrate the theoretical ones which the authors obtained recently. We also compute generalized eigenfunctions associated with the zero eigenvalue for the bifurcated solitary wave exhibiting a saddle-node bifurcation, and show that it does not change its stability type at the saddle-node bifurcation point.
We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger equations (CNLS) on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it a $textit{fu
High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a numerical sch
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generaliz
We study a class of nonlinear eigenvalue problems of Scrodinger type, where the potential is singular on a set of points. Such problems are widely present in physics and chemistry, and their analysis is of both theoretical and practical interest. In
The stability and dynamical properties of the so-called resonant nonlinear Schrodinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schrodinger (NLS) equation with the addition of a perturbation used to describe wave propag