Exact traveling waves solutions for long waves and blow-up phenomena

摘要

In this work we find exact traveling waves solutions to the fifth-order KDV-BBM type model that appear to describe the propagation of long waves in shallow water. We study the possibility of blow-up phenomenon of the fifth-order KDV-BBM type model under certain restrictions on the coefficients. Moreover, by applying the Ince transformation we also establish exact traveling waves solutions to the nonlinear evolution equation Benney-Lin type.