Conservation laws for a generalized Ito-type coupled KdV system

Edward Mogorosi, Ben Muatjetjeja, Chaudry Khalique
2012 Boundary Value Problems  
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 = U x , v = V x converts the generalized Ito-type coupled KdV system into a system of fourth-order partial differential equations in U and V variables, which
more » ... 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.
doi:10.1186/1687-2770-2012-150 fatcat:nbwuwsmsxrbupogqifcaxopmue