Conservation Laws for a Generalized Coupled Korteweg-de Vries System. (8th July 2013) - Nkwanazana, Daniel Mpho
Abstract : We construct conservation laws for a generalized coupled KdV system, which is a third-order system of nonlinear partial differential equations. We employ Noether's approach to derive the conservation laws. Since the system does not have a Lagrangian, we make use of the transformation u = U x, v = V x and convert the system to a fourth-order system in U, V . This new system has a Lagrangian, and so the Noether approach can now be used to obtain conservation laws. Finally, the conservation laws are expressed in the u, v variables, and they constitute the conservation laws for the third-order generalized coupled KdV system. Some local and infinitely many nonlocal conserved quantities are found.