Soliton and Periodic solutions of the Short Pulse Model Equation

Abstract

The short pulse (SP) equation is a novel model equation describing the propagation of ultra-short optical pulses in nonlinear media. This article reviews some recent results about the SP equation. In particular, we focus our attention on its exact solutions. By using a newly developed method of solution, we derive multisoliton solutions as well as 1-and 2-phase periodic solutions and investigate their properties.

Handbook of Solitons: Research, Technology and Applications edted by S.P. Lang and S.H. Bedore, Nova Publishers, New York, 2009, to appear

References in corpus (3)

• The short pulse equation is integrable
• Solitary wave solutions of the short pulse equation
• The Bi-Hamiltonian Structure of the Short Pulse Equation

Cited by in corpus (6)

• Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
• Integrable multi-component generalization of a modified short pulse equation
• A direct method for solving the generalized sine-Gordon equation
• The higher grading structure of the WKI hierarchy and the two-component short pulse equation
• Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations with Self-Consistent Sources: Geometry and Equivalence
• Self-adaptive moving mesh schemes for short pulse type equations and their Lax pairs