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 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.
CITATION STYLE
Mogorosi, E. T., Muatjetjeja, B., & Khalique, C. M. (2012). Conservation laws for a generalized Ito-type coupled KdV system. Boundary Value Problems, 2012(1). https://doi.org/10.1186/1687-2770-2012-150
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