Existence Of Periodic Traveling Wave Solutions For Several Kinds Of Nonhomogeneous Partial Differential Equations

This paper is divided into four chapters,and mainly discusses the existence of periodic traveling wave solutions for several non-homogeneous partial differential equations.Chapter 1 mainly describes the research status of the existence of periodic traveling wave solutions for various generalized BBM equations,KdVB equations and generalized Boussinesq equations.In addition,we give the main research methods of this paper.Chapter 2 investigates the existence of periodic traveling wave solution for generalized non-homogeneous BBM equation(p(u))t +(f(u))x + ?uxx + ?uxxt + ku = h(x-?t),x ? R,t ? 0,and the generalized non-homogeneous KdVB equation(p(u))t +(f(u))x + ?uxx + ?uxx + ku ? h(x-?),x ?R,t ? 0,where ?,??? are all no-zero constants;p,f ? C1(R),g,h ? C(R);h is non-identically zero,2T-periodic for some(T>0)with the property(?)By solving the Green's function,the periodic boundary value problems are transformed to the corresponding integral equations.Finally,using fixed point theorem,we obtain the existence of periodic traveling wave solutions.Our results generalize and improve the existing results.Chapter 3 studies the existence of periodic traveling wave solution for generalized non-homogeneous Boussinesq equation utt +[f(u)]tt-uxx +[g(u)xx + uxxxx = h(x-?t),where u = u(t,x),f,g,h E C2(R);h is non-identically zero,2T-periodic for some(T>0)with? the property r2T(?)By using the Green's function method and fixed point theorem,we obtain the existence of the periodic traveling wave solution.Chapter 4 summarizes the results obtained in the first two chapters and gives the ideas of the subsequent work.