The short pulse equation: Bäcklund transformations and applications
Hui Mao, Q.P. Liu
Abstract
Abstract A Bäcklund 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 of ‐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.
Topics & Concepts
BreatherSuperposition principleMathematicsTransformation (genetics)Pulse (music)Nonlinear systemMathematical analysisApplied mathematicsPhysicsQuantum mechanicsChemistryGeneVoltageBiochemistryNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Fiber Laser Technologies