Existence and computation of periodic travelling-wave solutions of a dispersive system. (English) Zbl 1254.35047
Summary: We establish existence of periodic travelling-wave solutions to a generalized Boussinesq system by using the topological degree theory for positive operators defined on a cone in an appropriate Banach space. Furthermore, we derive a high-accuracy pseudospectral solver based on a Fourier decomposition to construct numerical approximations of these stationary solutions. The numerical simulations are in perfect agreement with the theoretical results and new travelling-wave solutions of the system are computed which do not belong to the family of solutions proved to exist.
MSC:
35C07 | Traveling wave solutions |
35Q53 | KdV equations (Korteweg-de Vries equations) |
65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |