Convergence of the solutions of the BBM-KP and the BBM model equations

TL;DR

This paper proves that solutions of the BBM-KP equation converge to those of the BBM equation under certain conditions, highlighting the relationship between these models in a specific function space.

Contribution

It establishes the convergence of solutions from the BBM-KP equation to the BBM equation as the transverse variable tends to infinity, underlining a new connection between these models.

Findings

Solution convergence in a suitable function space

Convergence occurs when initial data are close as y → ±∞

Provides theoretical foundation for model approximation

Abstract

It is shown that the solution of the Cauchy problem for the BBM-KP equation converges to the solution of the Cauchy problem for the BBM equation in a suitable function space whenever the initial data for both equations are close as the transverse variable $y \rightarrow \pm \infty$.