New connections between moving curves and soliton equations

2001/04/30 by S. Murugesh, Radha Balakrishnan · 60 citations
Mathematics · Physics and Astronomy · #Geometry #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Numerical methods for differential equations #Physics #Quantum mechanics #Soliton #nlin.PS

paper · pdf · doi:10.1016/s0375-9601(01)00632-6

published in Physics Letters A 290(1-2), 81-87 (Elsevier BV) · some minor corrections made. 17 pages. Accepted in Phys. Lett. A

arxiv created 2001/10/03 · openalex publication_date 2001/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Lamb has identified a certain class of moving space curves with soliton equations. We show that there are two other classes of curve evolution that may be so identified. Hence three distinct classes of curve evolution are associated with a given integrable equation. The nonlinear Schrödinger equation is used to illustrate this explicitly.

Citations

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