Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Cam assa-Holm equation. We require that this generalization be, at the same tim e, integrable and physically derivable under the same asymptotic analysis a s the original Camassa-Holm equation. First, we find the equation in a pert urbative calculation in shallow-water theory. We then demonstrate its integ rability and find several particular solutions describing (2+1) solitary-wa ve like solutions. (C) 1999 Published by Elsevier Science B.V. All rights r eserved.