Conservation Laws for a Generalized Coupled Korteweg-de Vries System

الملخص EN

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=Ux, v=Vx 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.