Multilinear operators: the natural extension of Hirota's bilinear formalism

DOI10.1016/0375-9601(94)90367-0zbMath0910.58016arXivsolv-int/9404006OpenAlexW3105263763MaRDI QIDQ1336084

Alfred Ramani, Basile Grammaticos, Jarmo Hietarinta

Publication date: 14 October 1994

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

Full work available at URL: https://arxiv.org/abs/solv-int/9404006

zbMATH Keywords

integrabilitygauge invariancemultilinear operatorsHirota's bilinear formalismLax hierarchyHirota's bilinear \(D\) operatorSatsuma's lowest-order gauge invariant equationtrilinear case

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Soliton solutions of \(q\)-Toda lattice by Hirota direct method, New type of multiple lump and rogue wave solutions of the \((2+1)\)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili equation, Non-auto Bäcklund transformation, nonlocal symmetry and CRE solvability for the Bogoyavlenskii-Kadomtsev-Petviashvili equation, Trilinear equations, Bell polynomials, and resonant solutions, A direct bilinear Bäcklund transformation of a \((2+1)\)-dimensional Korteweg-de Vries-like model, Inelastic interaction solutions between multiple-lump molecule and kink solitons of the (2+1)-dimensional BKP equation, Algebraic invariants and generalized Hirota derivatives., Transvectants, modular forms, and the Heisenberg algebra., Zeros and amoebas of partition functions, Hirota’s Bilinear Method and Its Connection with Integrability, Complexity reduction for sign configurations through the KP II equation and its information-theoretic aspects, The Bogoyavlenskii-Schiff hierarchy and integrable equations in \((2+1)\) dimensions

Cites Work

• Unnamed Item
• Modifying Lax equations and the second Hamiltonian structure
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• A search for integrable bilinear equations: The Painlevé approach
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Soliton solutions and the higher order Korteweg–de Vries equations
• A search for bilinear equations passing Hirota’s three-soliton condition. IV. Complex bilinear equations