A Geometric Method to Investigate Prolongation Structures for Differential Systems With Applications to Integrable Systems

Details A Geometric Method to Investigate Prolongation Structures for Differential Systems With Applications to Integrable Systems A Geometric Method to Investigate Prolongation Structures for Differential Systems With Applications to Integrable Systems

2011-11-22

arxiv.org/abs/1111.5067v1

Physics

Mathematical Physics

16

Scientific paper

A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability condition corresponds to the Lie-algebra of SL (2,R), O(3), or SU(3). Each will be considered in turn and the latter two systems represent larger 3by3 cases. This geometric approach is applied to all three of these systems to obatin prolongation structures explicitly. In both 3by3 cases the prolongation structure is reduced to the situation of three smaller 2by2 problems. Many types of conservation laws can be obtained at different stages of the development, and at the end, a single result is developed to show how this can be done.

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