The short pulse equation: Backlund transformations and applications

摘要

A Backlund transformation (BT), which involves both independent and dependent variables, is established and studied for the short pulse (SP) equation. Based it, the nonlinear superposition formulae for 2-, 3-, and 4-BT are presented. The general result for the composition ofN-BTs is achieved and given in terms of determinants. As applications, various solutions including loop solitons, breather solutions, and their interaction solutions are worked out.