Singular solitons and numerical analysis of Φ–four equation

Title: Numerical Analysis of a Singular Integral Equation

Singular solitons and bifurcation analysis of quadratic nonlinear Klein-Gordon equation

This paper studies the Klein-Gordon equation with quadratic nonlinearity. The ansatz approach is used to first obtain the singular soliton solution of the equation along with the corresponding domain restriction. The bifurcation analysis is also carried out. By this analysis, a few more traveling wave solutions are retrieved. The bifurcation phase portraits are also given.

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

Numerical Analysis of Stability for Temporal Bright Solitons in a PT-Symmetric NLDC

PT-Symmetry is one of the interesting topics in quantum mechanics and optics. One of the demonstration of PT-Symmetric effects in optics is appeared in the nonlinear directional coupler (NLDC). In the paper we numerically investigate the stability of temporal bright solitons propagate in a PT-Symmetric NLDC by considering gain in bar and loss in cross. By using the analytical solutions of pertu...

Numerical analysis on singular solutions of the Poisson equation in two-dimensions

A numerical method for extracting the coef®cients of the asymptotic series solution of the Poisson equation in two dimensions in the vicinity of singular points is presented. This method is an extension of that presented in (Szabo and Yosibash 1996) to non-homogeneous boundary value problems, and is general in the sense that it is applicable to almost any type of point singularity. Numerical e...