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Mogorosi, Edward Tshepo; Muatjetjeja, Ben; Khalique, Chaudry Masood

Conservation laws for a generalized Ito-type coupled KdV system. (English) Zbl 1278.35199

Bound. Value Probl. 2012, Paper No. 150, 7 p. (2012).
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.

Cited in 3 Documents

MSC:

35Q35 PDEs in connection with fluid mechanics
35A30 Geometric theory, characteristics, transformations in context of PDEs
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