1 research outputs found
Lax pairs, Painlev\'e properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation
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 Painlev\'e property.
Some exact solutions are also constructed