Bilinearization and Special Solutions to the Discrete Schwarzian KdV Equation

2011/02/09 by Mike Hay, Hay, Mike, Kenji Kajiwara +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1102.1829

openalex publication_date 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda lattice equations. We then construct two kinds of solutions in terms of the Casorati determinant. We derive the discrete Schwarzian KdV equation on an inhomogeneous lattice and its solutions by a reduction process. We finally discuss the solutions in terms of the τ functions of some Painlevé systems.

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