Constructing lump-like solutions of the Hirota–Miwa equation
| Autor: | B. Grammaticos, Vassilios G. Papageorgiou, Alfred Ramani, Ralph Willox, Junkichi Satsuma |
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| Rok vydání: | 2007 |
| Předmět: |
Statistics and Probability
Polynomial Variables media_common.quotation_subject Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics Kadomtsev–Petviashvili equation Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Modeling and Simulation Applied mathematics Limit (mathematics) Soliton Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics media_common Mathematics Ansatz Gramian matrix |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 40:12619-12627 |
| ISSN: | 1751-8121 1751-8113 |
| DOI: | 10.1088/1751-8113/40/42/s08 |
| Popis: | We construct special solutions of the Hirota–Miwa equation for which the τ-function is a polynomial in the independent variables. Three different methods are presented: direct construction (obtained also as a limit of the soliton solutions), and the derivation of the solutions in two different determinant forms, namely Grammian and Casorati. Introducing the appropriate ansatz, we write the Hirota–Miwa equation in a nonlinear form for a single variable. In terms of the latter, the solutions obtained are rational and are reminiscent of the lump solutions for the continuous analogue of the Hirota–Miwa equation, namely the KP equation. |
| Databáze: | OpenAIRE |
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