Elliptic N-soliton Solutions of ABS Lattice Equations

DOI10.1093/imrn/rnq010zbMath1217.37068arXiv0911.0461OpenAlexW2021845526MaRDI QIDQ3057524

James R. Atkinson, Frank W. Nijhoff

Publication date: 24 November 2010

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.0461

zbMATH Keywords

Bäcklund transformationspartial differential equationsquadrilateral lattice equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Discrete version of topics in analysis (39A12) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Lattice dynamics; integrable lattice equations (37K60)

Related Items (16)

Elliptic soliton solutions: \(\tau\) functions, vertex operators and bilinear identities ⋮ Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach ⋮ Discrete solitons in infinite reduced words ⋮ Two trigonometric function solutions of the mKdV equations ⋮ Addition formulae, Bäcklund transformations, periodic solutions, and quadrilateral equations ⋮ Integrable quad equations derived from the quantum Yang-Baxter equation ⋮ Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation ⋮ Discrete analogues for two nonlinear Schrödinger type equations ⋮ Elliptic solutions of Boussinesq type lattice equations and the elliptic \(N\)th root of unity ⋮ The Sylvester equation and the elliptic Korteweg-de Vries system ⋮ On one-soliton solutions of the Q2 equation in the ABS List ⋮ Direct Linearization of Extended Lattice BSQ Systems ⋮ A constructive approach to the soliton solutions of integrable quadrilateral lattice equations ⋮ The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation ⋮ Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps ⋮ Symmetric discrete AKP and BKP equations

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