FIZIKA A 18 (2009) 1 , 2944
THE EXACT SOLUTIONS TO LIENÁRD EQUATION WITH HIGHORDER NONLINEAR TERM AND APPLICATIONS
LIU CHENGSHI
Department of Mathematics, Daqing Petroleum Institute, Daqing 163318, China
Email address: chengshiliu68@126.com
Received 17 August 2008; Accepted 3 June 2009
Online 13 July 2009
Using the complete discrimination system for polynomials, we give the exact
solutions to Lienárd equation with strong highorder nonlinear terms which
include the elementary functions solutions, elliptic functions solutions and the
solutions expressed with implicit functions. As application, we can easily
obtain many exact solutions to some nonlinear equations of mathematical physics
such as Kundu equation, generalized PC equation, Ablowitz equation, RangwalaRao
equation, generalized BBM equation, generalized PochhammerChree equation
without dispersion term and generalized GinzburgLandau equation. To our
knowledge, the known results on the exact travelling solutions to these
equations in literature can be derived from our results as special cases.
PACS numbers: 02.30.Jr, 05.45.Yv
UDC 532.591, 533.951
Keywords: Lienárd equation; complete discrimination system for polynomial,
traveling wave solution, exact solution, nonlinear evolution equation
