Infinitely many nonlocal conservation laws for the $ABC$ equation with $A+B+C\ne 0$

Abstract

We construct an infinite hierarchy of nonlocal conservation laws for the $ABC$ equation $A{u}_t{u}_{xy}+B{u}_x{u}_{ty}+C{u}_y{u}_{tx}=0$, where $A,B,C$ are constants and $A+B+C\ne 0$, using a nonisospectral Lax pair. As a byproduct, we present new coverings for the ABC equation. The method of proof of nontriviality of the conservation laws under study is quite general and can be applied to many other integrable multidimensional systems.

10 pages, no figures, slightly revised and extended version

References in corpus (3)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Conservation laws and normal forms of evolution equations
• Veronese webs and nonlinear PDEs

Cited by in corpus (4)

• On a classification algorithm of the integrable two-dimensional lattices via Lie-Rinehart algebras
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• On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems
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