A geometrical demonstration for continuation of solutions of the generalised BBM equation

TL;DR

This paper provides a geometric proof demonstrating that solutions of the generalized BBM equation that vanish on an open set must be identically zero, establishing the uniqueness of compactly supported solutions.

Contribution

It introduces a geometric demonstration for the continuation property of solutions to the generalized BBM equation, highlighting the uniqueness of solutions with compact support.

Findings

Solutions vanishing on an open set are identically zero

The only compactly supported solution is the trivial solution

Provides a simple geometric proof for solution continuation

Abstract

A simple proof that if the generalised BBM equation has a solution vanishing on an open sent of its domain then the solution is necessarily zero is given. In particular, the only compactly supported solution of the equation under consideration is the identically vanishing one.