Exterior Differential Systems, Prolongations and the Integrability of Two Nonlinear Partial Differential Equations

Details Exterior Differential Systems, Prolongations and the Integrability of Two Nonlinear Partial Differential Equations Exterior Differential Systems, Prolongations and the Integrability of Two Nonlinear Partial Differential Equations

2009-03-24

arxiv.org/abs/0903.4163v1

Physics

Mathematical Physics

22 pgs

Scientific paper

A generalized KdV equation is formulated as an exterior differential system, which is used to determine the prolongation structure of the equation. The prolongation structure is obtained for several cases of the variable powers, and nontrivial algebras are determined. The analysis is extended to a differential system which gives the Camassa-Holm equation as a particular case. The subject of conservation laws is briefly discussed for each of the equations. A Backlund transformation is determined using one of the prolongations.

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