Asymptotics in shallow water waves

Abstract

In this paper we consider the initial value problem for a family of shallow water equations on the line $\mathbb{R}$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as $x\to \pm \infty$ and prove their invariance with respect to the solution map.

References in corpus (1)

• Wave Structures and Nonlinear Balances in a Family of 1+1 Evolutionary PDEs