The Short Pulse Equation Is Integrable

2004/09/19 by Anton Sakovich, Sergei Sakovich · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Molecular spectroscopy and chirality #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP #nlin.SI #physics.optics

paper · pdf · doi:10.1143/jpsj.74.239

published as J. Phys. Soc. Jpn. 74 (2005) 239-241 · 7 pages

arxiv created 2004/09/19 · openalex publication_date 2005/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We prove that the Schäfer–Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses in nonlinear media is integrable. First, we discover a Lax pair of the SPE which turns out to be of the Wadati–Konno–Ichikawa type. Second, we construct a chain of transformations which relates the SPE with the sine-Gordon equation. 1

Citations

• Cyclic Bases of Zero-Curvature Representations: Five Illustrations to One Concept
• On integrability of one third-order nonlinear evolution equation

Cited by

• On the Polysymplectic Integrator for the Short Pulse Equation
• Cauchy problem and multi-soliton solutions for a two-component short pulse system
• Soliton Resolution for the Short-pluse Equation

Related

• Soliton and Periodic solutions of the Short Pulse Model Equation
• On the Polysymplectic Integrator for the Short Pulse Equation
• The Short Pulse Hierarchy
• Long-time asymptotics for the short pulse equation
• Asymptotic integrability and its consequences