Bilinearization of discrete soliton equations and singularity confinement.

DOI10.1016/S0375-9601(97)00171-0zbMath1043.35520arXivsolv-int/9610005OpenAlexW1970291045WikidataQ126389165 ScholiaQ126389165MaRDI QIDQ1968267

Masayuki Oikawa, Shinichiro Nakao, Ken-Ichi Maruno, Kenji Kajiwara

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9610005

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) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (16)

Integrable delay-difference and delay-differential analogs of the KdV, Boussinesq, and KP equations ⋮ A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations ⋮ Rational solutions to Q3 _δ in the Adler-Bobenko-Suris list and degenerations ⋮ Ultradiscrete Miura transformation ⋮ Bilinear Forms of Integrable Lattices Related to Toda and Lotka-Volterra Lattices ⋮ Rational solutions to the ABS list: transformation approach ⋮ Integrable discretizations and soliton solution of KdV and mKdV equations ⋮ Casorati determinant solution for the discrete-time relativistic Toda lattice equation ⋮ Lax representations and integrable time discretizations of the DDKdV, DDmKdV, and DDHOKdV ⋮ Asymmetric integrable quad-graph equations ⋮ The discrete potential Boussinesq equation and its multisoliton solutions ⋮ Soliton-antisoliton collision in the ultradiscrete modified KdV equation ⋮ Integrability in a discrete world ⋮ Bilinearization of discrete soliton equations through the singularity confinement test ⋮ Bilinear structure and determinant solution for the relativistic Lotka-Volterra equation ⋮ Lax integrable nonlinear partial difference equations

Cites Work

• On Hirota's difference equations
• Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• Bilinear discrete Painleve equations
• Conserved Quantities of a Class of Nonlinear Difference-Difference Equations
• Casorati and Discrete Gram Type Determinant Representations of Solutions to the Discrete KP Hierarchy
• Do integrable mappings have the Painlevé property?

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