On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain

2025/05/27 by I. T. Habibullin, Habibullin, I. T., A. R. Khakimova +1 · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Chain (unit) #Class (philosophy) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Integrable system #Lie algebra #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Simple (philosophy) #Toda lattice #nlin.SI

paper · pdf · doi:10.48550/arxiv.2505.20786

openalex publication_date 2025/05/27 · arxiv published 2025/05/27 · arxiv updated 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the method is exemplified by the equation DS I, for which a new class of explicit solutions is constructed, containing freedom in two arbitrary functions. In this case the generalized Toda lattice corresponding to the simple Lie algebra A₂ is used as a dressing chain.

Citations

• On a class of exact solutions of the Ishimori equation
• The finite gap method and the periodic Cauchy problem of 2+1 dimensional anomalous waves for the focusing Davey-Stewartson 2 equation
• On three-dimensional packets of surface waves

Cited by

• Discrete integrable equations with three independent variables

Discussions

• I. T. Habibullin, A. R. Khakimova: On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain https://arxiv.org/abs/2505.20786 https://arxiv.org/pdf/2505.20786 https [bsky, 0 points, 1 comments]

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