Explicit Travelling Wave Solutions And Stability Properties For A Class Of Nonlinear Evolution Equations

Nonlinear partial differential equations(NLPDEs)are often used to describe many nonlinear phenomena in engineering,science,nature,and other fields.Finding solutions to NLPDEs has attracted a large number of engineers,physicists,and mathematicians in the field of nonlinear science.For this reason,many methods for solving nonlinear par-tial differential equations have been invented.However,so far,none of the methods are applicable to all equations.In this thesis,Khater's method,a new method for solving NLPDEs,is proposed.Many existing methods can be taken as its special cases,and four methods are used to construct the exact travelling wave solutions and solitary wave solutions of some nonlinear par-tial differential equations(including rational forms,periodic solutions,kinks,and anti-kink families,spikes,cuspons,etc.).The improved and novel(G'/G)-expansion meth-ods are applied to the fractional order biological population model,the time fractional Burgers equation,the Drinfel'd-Sokolov-Wilson equation,the system of shallow-water wave equations,the nonlinear complex fractional Kundu-Eckhaus equation,the nonlin-ear complex fractional Schrodinger equation,the two-dimensional nonlinear Kadomt-sev-Petviashvili Burgers equation,and the three-dimensional modified Zakharov-Kuznetsov equation for constructing new explicit solutions.The extended simplest equa-tion method is used to evaluate the travelling wave solutions of the generalized Radhakr-ishnan-Kundu-Lakshmanan equation,the pressure equation of bubbly liquids,the two-dimensional nonlinear Kadomtsev-Petviashvili Burgers equation,and the three-dimen-sional modified Zakharov-Kuznetsov equation.Also,the modified Khater method is em-ployed to detect the new computational solutions of the(2+1)-dimensional Konopelchenko-Dubrovsky equation,the KdV equation,the fractional biological Population model,the fractional equal width model,the fractional modified equal width equation,and the non-linear fractional Wu-Zhang system.Many of these solutions have been found for the first time.Additionally,the stability property for the obtained solutions is investigated by using the Hamiltonian system properties.The results obtained in this thesis show that the Khater method is an effective method for solving NLPDEs,and it has strong practicability.The new solutions of some nonlinear partial differential equations obtained by us provide a theoretical basis for the application of these equations.