非线性薛定谔方程的差分格式
Difference Scheme of Nonlinear Schr?dinger Equation
摘要:
非线性薛定谔方程是目前最为活跃的研究课题之一，被广泛应用在生物医学、高能物理、量子力学以及非线性光学等很多领域，当我们想了解这些现象的原理时，就需要对非线性薛定谔方程的解进行研究。本文对一类非线性薛定谔方程的周差分格式进行了探究，对方程我们提出了一种非线性差分格式，证明了这个差分格式满足能量守恒定律和质量守恒定律，并且在这基础上验证了差分格式解的存在性问题。
Abstract:
The nonlinear Schrödinger equation is one of the most active research topics at present, it is widely used in many fields such as biomedicine, high energy physics, quantum mechanics and nonlinear optics. When we want to understand the principles of these phenomena, it is necessary to study the solution of the nonlinear Schrödinger equation. This paper explores the week difference scheme of a class of nonlinear Schrödinger equation, we propose a nonlinear difference scheme for the equation, it is proved that this difference scheme satisfies the law of conservation of mass. And on this basis, the existence of the solution of the difference scheme is verified.
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