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Z. Naturforsch. 69a, 489 – 496
(2014)
doi:10.5560/ZNA.2014-0037
Group Invariant Solutions and Conservation Laws of the Fornberg–Whitham Equation
Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab 55517, Iran
Received May 22, 2013 / revised May 2, 2014 / published online July 16, 2014
Reprint requests to: M. S. H.; E-mail:
hashemi@bonabu.ac.ir,
hashemi_math396@yahoo.com
In this paper, we utilize the Lie symmetry analysis method to calculate new solutions for the Fornberg–Whitham equation (FWE). Applying a reduction method introduced by M. C. Nucci, exact solutions and first integrals of reduced ordinary differential equations (ODEs) are considered. Nonlinear self-adjointness of the FWE is proved and conserved vectors are computed.
Key words: Lie Symmetry; First Integral; Nonlinear Self-Adjointness; Conservation Law.
PACS numbers: 02.20.-a; 02.20.Sr; 02.30.Jr; 11.30.-j
Mathematics Subject Classification 2000: 58J70; 76M60; 70H33; 70S10