The short pulse equation and associated constraints
arXiv:0906.1536 · doi:10.1088/1751-8113/42/44/442004
Abstract
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.