On effective solutions of the nonlinear Schr?dinger equation

Physics and Mathematics of Nonlinear Phenomena 2013

Khatiashvili, N.^1 ; Shanidze, R.^1 ; Janjgava, D.^1

I. Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, University St., 2, 0186 Tbilisi, Georgia^1

关键词: Approximated solutions;    Dinger equation;    Effective solution;    Equivalent system;    Infinite domains;    New functions;    Non-linear elliptic equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012020/pdf
DOI  :  10.1088/1742-6596/482/1/012020

来源: IOP

【 摘 要 】

Cubic nonlinear Schrodinger type equation with specific initial-boundary conditions in the infinite domain is considered. The equation is reduced to an equivalent system of partial differential equations and studied in the case of solitary waves. The system is modified by introducing new functions, one of which belongs to the class of functions of negligible fifth order and vanishing at infinity exponentially. For this class of functions the system is reduced to a nonlinear elliptic equation which can be solved analytically, thereby allowing us to present nontrivial approximated solutions of nonlinear Schrodinger equation. These solutions describe a new class of symmetric solitary waves. Graphics of modulus of the corresponding wave function are constructed by using Maple.