Articles

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

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,

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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