Theoretical and numerical results for the nonlinear shallow water problem

Abstract

In this paper, the nonlinear shallow water problem is studied analytically and numerically. This problem has been studied by different authors in the linear case; here we consider a nonlinear one with non constant coefficients. We first start by a mathematical analysis, where the well posedness is proved via the use of traveling wave solutions. The existence and uniqueness of the solution is demonstrated by the means of Schaulder's and Banach's fixed point theorems. Then, we explore the proposed model and investigate the stability conditions and the efficiency numerically.

Keywords

• shallow water model
• traveling wave solutions
• well posedness
• finite differences