Articles

Variational approaches to conservation laws for a nonlinear evolution equation with time dependent coefficients

Published in: Quaestiones Mathematicae
Volume 34 , issue 2 , 2011 , pages: 235–245

DOI: 10.2989/16073606.2011.594238

Author(s): A.G. Johnpillai Department of Mathematics, Sri Lanka , C.M. Khalique International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, South Africa

Keywords: 35Q53 , 37K10 , 37K35 , 35L65 , 35Q53 , 37K10 , 37K35 , 35L65

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Abstract

The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to the Noether theorem to determine the conservation laws. We utilize the new conservation theorem (N.H. Ibragimov, [8]) and the partial Lagrangian approach (A.H. Kara, F.M. Mahomed, [13]) to construct local, and infinite number of nonlocal conservation laws (due to the transformation of the dependent variable) of the underlying equation.

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