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Two-dimensional integrable generalization of the Camassa–Holm equation

Authors
Journal
Physics Letters A
0375-9601
Publisher
Elsevier
Publication Date
Volume
260
Identifiers
DOI: 10.1016/s0375-9601(99)00536-8

Abstract

Abstract In this letter we discuss the (2+1)-dimensional generalization of the Camassa–Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa–Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2+1) solitary-wave like solutions.

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