Integrability of Certain Deformed Nonlinear Partial Differential Equations

Abstract

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point of complete integrability, is presented. Following the procedure of Ablowitz, Kaup, Newell and Segur (AKNS) we find that the deformed version of Nonlinear Schrodinger equation, Hirota equation and AKNS equation admit Lax pairs. We report that each of the identified deformed equations possesses the Painlev property for partial differential equations and admits trilinear representation obtained by truncating the associated Painlev expansions. Hence the above mentioned deformed equations are completely integrable.