A Note on Exact Traveling Wave Solutions for SomeNonlinear Systems

Abstract

We mainly study two papers "New exact travelling wave solutions of two nonlinear physical models" written by S A El-Wakil and M A Abdou and "The periodic wave solutions for two systems of nonlinear wave equations" written by Wang Ming-Liang Wang Yue-Ming and Zhang Jin-Liang then we explore the methods used in the article and use them to find the exact traveling wave solutions of some partial differential equations In this paper we introduced several different partial differential equations and use an improved tanh function method and computer symbolic calculation to find exact travelling wave solutions for some nonlinear systems including Zakharov equations KdV equations etc and the approximate solution of Quantum Zakharov equations Then substitute some proper parameters and then use the Mathematica to draw the solution graphs These tell us that the equations have different types of solutions and they have their own physical meanings In the process we will learn more about the commonalities between partial differential equations and we will describe and introduce them in detail in the derivation process The main idea of this method is to take full advantage of the family of Riccati equation which has more solutions The exact solutions obtained are including new soliton-like solutions trigonometric function solutions and rational solutions Finally I added some solutions that the author did not presented and corrected some errors on Wikipedia to make the results more complete

Date of Award	2021
Original language	English
Supervisor	Yung-Fu Fang (Supervisor)