2001/10/01 by Richard Beals, D. H. Sattinger, Jacek Szmigielski · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential equation #Geometry #Hierarchy #Integrable system #Inverse #Inverse problem #Inverse scattering problem #Inverse scattering transform #Law #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Partial differential equation #Physics #Piecewise #Pure mathematics #Quantum inverse scattering method #Scattering
paper · doi:10.1080/00036810108840938
openalex publication_date 2001/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The nonlinear partial differential equation was proposed by Hunter and Saxton as an asymptotic model equation for nematic liquid crystals. Hunter and Zheng showed that it is a member of the Harry Dym hierarchy of integrable flows, and solved the equation explicitly for a family of finite dimensional, piecewise linear functions in the case when ux has compact support. In this note, the associated inverse scattering problem is used to obtain the explicit solutions of the finite dimensional flows in both the compact and non-compact case.