The short pulse equation and associated constraints

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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Scientific paper

10.1088/1751-8113/42/44/442004

The short pulse equation (SPE) is considered as an initial-boundary value
problem. It is found that the solutions of the SPE must satisfy an integral
relation otherwise the temporal derivative exhibits discontinuities. This
integral relation is not necessary for a solution to exist. An infinite number
of such constraints can be dynamically generated by the evolution equation.

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