Backlund transformations of MKdV and Painleve equations

1993/05/19 by Jeremy Schiff, J Schiff · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #nlin.SI #solv-int

paper · pdf · doi:10.1088/0951-7715/7/1/015

8 pages, plain tex

arxiv created 1993/05/19 · openalex publication_date 1994/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

For N>or=3 there are S N and D N actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z 2 actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painleve equations.

Citations

• Unitary Matrix Models and 2D Quantum Gravity (Virasoro constraints modified)

Cited by

• A dynamical systems approach to the fourth Painlevé equation
• A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems