Two-dimensional integrable generalization of the Camassa-Holm equation

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1999-12-01

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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. © 1999 Published by Elsevier Science B.V. All rights reserved.

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Physics Letters, Section A: General, Atomic and Solid State Physics, v. 260, n. 3-4, p. 218-224, 1999.