Conservation Laws for a Generalized Coupled Korteweg-de Vries System
Keyword(s):
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 transformationu=Ux,v=Vxand convert the system to a fourth-order system inU,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 theu,vvariables, and they constitute the conservation laws for the third-order generalized coupled KdV system. Some local and infinitely many nonlocal conserved quantities are found.
2014 ◽
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Keyword(s):
2018 ◽
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