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Journal of Nonlinear Mathematical Physics Volume 17, 2010 - Issue 3
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Articles

INTEGRABILITY OF CERTAIN DEFORMED NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

R. SAHADEVAN Ramanujan Institute For Advanced Study in Mathematics, University of Madras, Chennai-600 005, Tamil Nadu, India
&
L. NALINIDEVI Ramanujan Institute For Advanced Study in Mathematics, University of Madras, Chennai-600 005, Tamil Nadu, India
Pages 379-396 | Published online: 04 Mar 2013
 
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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 Painlevé property for partial differential equations and admits trilinear representation obtained by truncating the associated Painlevé expansions. Hence the above mentioned deformed equations are completely integrable.

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