GLIDE OF STANDING SOLITARY WAVE IN AN INCLINED LONG WATER TROUGH

Abstract

A NLS-type equation with an additional term of variable coefficient governing the modulational evolution of standing gravity waves on a water layer with slowly variable depth is obtained by using the multiple scale method to the potential-flow boundary value problem. A single solitary wave solution of this equation, that corresponds to the standing solitary wave observed by Wu et al. in a slightly inclined rectangular water trough, is given. It is found that such solitary wave moves slowly, with an acceleration, toward the shallow region.