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Conservation laws for a generalized Ito-type coupled KdV system

Edward Tshepo Mogorosi, Ben Muatjetjeja* and Chaudry Masood Khalique

Author Affiliations

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, P. Bag X2046, Mmabatho, 2735, Republic of South Africa

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Boundary Value Problems 2012, 2012:150  doi:10.1186/1687-2770-2012-150

Published: 28 December 2012


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 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/150/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/150/mathml/M1">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/150/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/150/mathml/M2">View MathML</a> 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.