Original scientific paper
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
Abstract
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.
Keywords
Lienárd equation; complete discrimination system for polynomial; traveling wave solution; exact solution; nonlinear evolution equation
Hrčak ID:
302561
URI
Publication date:
1.3.2009.
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