Analytic Solutions To A Class Of Nonlocal NLS Type Equations

Nonlinear partial differential equations can describe natural phenomena in water waves,optics,bose-einstein condensation,electromagnetism and plasma.In 2013,Abloitz constructed and studied the integrable nonlocal nonlinear schrodinger(NLS)equation.This paper mainly analyzes the solution of the nonlocal NLS equation,solves it by using bilinear method and KP reduction method,and gives the general expression.By taking appropriate values of the parameters in the solution,the first and second order solutions of NLS equations are obtained and their dynamic behaviors are analyzed.Furthermore,based on the characteristics of nonlocal NLS equations,this paper presents a coupled Ablowitz-Kaup-Newell-Segur(AKNS)system and the Lax pair of the system.Many nonlocal NLS equations are derived from the reduction of coupled AKNS systems.In this paper,a nonlocal two-place NLS equation is obtained by reduction of symmetric group.By studying this equation and discovering it PTC symmetric invariant one-soliton solution and periodic two-soliton solution,as well as the further study on the coupling AKNS system produced by the symmetry group reduced a four NLS equation of the local area,and get the symmetry group of the same double soliton solution.This paper further study a nonlocal four-place NLS equation that is obtained by symmetric group reduction of coupled AKNS system,and obtain its symmetric group invariant two-soliton solution.