Geometrical demonstration for persistence properties for a bi-Hamiltonian shallow water system

Abstract

We present a geometrical demonstration for persistence properties for a bi-Hamiltonian system modelling waves in a shallow water regime. Both periodic and non-periodic cases are considered and a key ingredient in our approach is one of the Hamiltonians of the system. As a consequence of our developments we improve recent works dealing with unique continuation properties for shallow water equations, as well as we provide a novel way to prove that the unique compactly supported solution of the system is necessarily the zero function.

Some theorems were proved based on false conditions. The mistakes have been corrected

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Cited by in corpus (4)

• Conserved quantities, continuation and compactly supported solutions of some shallow water models
• Existence, continuation, persistence and dynamics of solutions for a generalized 0-Holm-Staley equation
• Persistence properties of a Camassa-Holm type equation with $(n+1)-$order non-linearities
• Unique continuation results for abstract quasi-linear evolution equations in Banach spaces