A Study on Nonlinear Dispersive Partial Differential Equations By Rdt Method: Analyzing Numerical Methods for Nonlinear Dispersive Equations

Abstract

The nonlinear dispersiveequations, including a large body of classes, are widely used models for agreat number of problems in the fields of physics, chemistry and biology, andhave gained a surge of attention from mathematicians ever since they werederived. In addition to mathematical analysis, the numeric of these equationsis also a beautiful world and the studies on it have never stopped. The aim of this paper is topropose and analyze various numerical methods for some representative classesof nonlinear dispersive equations, which mainly arise in the problems ofquantum mechanics and nonlinear optics. Extensive numerical results are alsoreported, which are geared towards demonstrating the efficiency and accuracy ofthe methods, as well as illustrating the numerical analysis and applications.Although the subjects considered here is merely a small sample of nonlineardispersive equations, it is believed that the methods and results achieved forthese equations can be applied or extended to more general cases.