Exterior Differential Systems Prolongations and Application to a Study of Two Nonlinear Partial Differential Equations
A generalized Korteweg-de Vries 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 Bäcklund transformation is determined using one of the prolongations.
Bracken, P. Exterior Differential Systems Prolongations and Application to a Study of Two Nonlinear Partial Differential Equations. Acta Appl Math 113, 247–263 (2011). https://doi.org/10.1007/s10440-010-9597-z
Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications