An Application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
| Autor: | Shi-Hao Li, Xiang-Ke Chang, Jun-Xiao Zhao, Xing-Biao Hu |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
37K10 35Q51 15A15 Integrable system Nonlinear Sciences - Exactly Solvable and Integrable Systems General Mathematics 010102 general mathematics FOS: Physical sciences Pfaffian Mathematical Physics (math-ph) 01 natural sciences Peakon Nonlinear system Isospectral Quadratic equation Nonlinear Sciences::Exactly Solvable and Integrable Systems 0103 physical sciences Novikov self-consistency principle 010307 mathematical physics 0101 mathematics Exactly Solvable and Integrable Systems (nlin.SI) Toda lattice Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1712.00965 |
| Popis: | The Novikov equation is an integrable analogue of the Camassa-Holm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this paper, an approach involving Pfaffians is applied to study multipeakons of the Novikov equation. First, we show that the Novikov peakon ODEs describe an isospectral flow on the manifold cut out by certain Pfaffian identities. Then, a link between the Novikov peakons and the finite Toda lattice of BKP type (B-Toda lattice) is established based on the use of Pfaffians. Finally, certain generalizations of the Novikov equation and the finite B-Toda lattice are proposed together with special solutions. To our knowledge, it is the first time that the peakon problem is interpreted in terms of Pfaffians. Comment: 33pages |
| Databáze: | OpenAIRE |
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