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Conservation laws for a generalized Ito-type coupled KdV system

Research paper by Edward Tshepo Mogorosi, Ben Muatjetjeja, Chaudry Masood Khalique

Indexed on: 28 Dec '12Published on: 28 Dec '12Published in: Boundary Value Problems



Abstract

In this paper, the conservation laws for a generalized Ito-type coupled Korteweg-de Vries (KdV) system are constructed by increasing the order of the partial differential equations. The generalized Ito-type coupled KdV system is a third-order system of two partial differential equations and does not have a Lagrangian. The transformation u=Ux, v=Vx converts the generalized Ito-type coupled KdV system into a system of fourth-order partial differential equations in U and V variables, which has a Lagrangian. Noether’s approach is then used to construct the conservation laws. Finally, the conservation laws are expressed in the original variables u and v. Some local and infinitely many nonlocal conserved quantities are found for the generalized Ito-typed coupled KdV system.