The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed system of integral differential equations and a non- linear scalar integral differential equation. It wi...The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed system of integral differential equations and a non- linear scalar integral differential equation. It will be shown that there exist six standing wave solutions （（u（x,t）,w（x,t）） = （U（x）,W（x）） to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave so- lutions u（x,t） = U（x） to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.展开更多
文摘The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed system of integral differential equations and a non- linear scalar integral differential equation. It will be shown that there exist six standing wave solutions （（u（x,t）,w（x,t）） = （U（x）,W（x）） to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave so- lutions u（x,t） = U（x） to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.
