Variational approaches to conservation laws for a nonlinear evolution equation with time dependent coefficients
AbstractThe 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, ) and the partial Lagrangian approach (A.H. Kara, F.M. Mahomed, ) 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.