Conservation laws for a generalized Ito-type coupled KdV system. (English) Zbl 1278.35199
Summary: 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 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.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
35A30 | Geometric theory, characteristics, transformations in context of PDEs |
References:
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