Lax pairs, Painlevé properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation

Abstract

We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV equation are integrable in the sense that they possess the Painlevé property. Some exact solutions are also constructed.

References in corpus (1)

• N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation

Cited by in corpus (1)

• The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients