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

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.

Quaestiones Mathematicae 34(2011), 235–245.