Resonant line solitons and localized excitations in a (2+1)-dimensional higher-order dispersive long wave system in shallow water

Abstract

In this work, we consider a (2+1)-dimensional higher-order dispersive long wave system that models dispersive long gravity waves in shallow water of finite depth. By transforming the variable separation solution into the $\tau$-function form, we effectively identify resonant line solitons and analyze their asymptotic behavior. Specifically, those resonant solitons include the $\left(3142\right)$-type solitons, T-type solitons, and O-type solitons in shallow water. In addition, we introduce two novel types of instanton excitations induced by dromion resonance. The first type is characterized by different growth and decay rates, while the second type exhibits an odd symmetry, described by $A(-x,y,-t)=-A(x,y,t)$. These solutions are applicable to other solvable nonlinear systems using the multilinear variable separation approach. It is hoped that the study will be helpful in the analysis of dispersive long gravity waves propagating in two horizontal directions, such as resonant line solitons on fluid surfaces and hydrodynamic instantons.