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FIZIKA A 18 (2009) 1 , 29-44
 
THE EXACT SOLUTIONS TO LIENÁRD EQUATION WITH HIGH-ORDER NONLINEAR TERM AND APPLICATIONS
LIU CHENG-SHI
Department of Mathematics, Daqing Petroleum Institute, Daqing 163318, China
E-mail address: chengshiliu-68@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 high-order 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, Rangwala-Rao
equation, generalized BBM equation, generalized Pochhammer-Chree equation
without dispersion term and generalized Ginzburg-Landau 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
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