Soliton solutions to the Sawada--Kotera equation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909783062216704 |
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| author | Aktosun, Tuncay Choque-Rivero, Abdon E. Toledo, Ivan Unlu, Mehmet |
| author_facet | Aktosun, Tuncay Choque-Rivero, Abdon E. Toledo, Ivan Unlu, Mehmet |
| contents | We consider the direct and inverse scattering problems for the third-order differential equation in the reflectionless case. We formulate a corresponding Riemann--Hilbert problem using input consisting of the bound-state poles of a transmission coefficient and the bound-state dependency constants. With the time-evolved dependency constants, using the solution to the Riemann--Hilbert problem, we construct soliton solutions to an integrable system of fifth-order nonlinear partial differential equations. By imposing some appropriate restrictions on the dependency constants, we show that those soliton solutions yield soliton solutions to the Sawada--Kotera equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soliton solutions to the Sawada--Kotera equation Aktosun, Tuncay Choque-Rivero, Abdon E. Toledo, Ivan Unlu, Mehmet Exactly Solvable and Integrable Systems 34A55 34M50 35C08 We consider the direct and inverse scattering problems for the third-order differential equation in the reflectionless case. We formulate a corresponding Riemann--Hilbert problem using input consisting of the bound-state poles of a transmission coefficient and the bound-state dependency constants. With the time-evolved dependency constants, using the solution to the Riemann--Hilbert problem, we construct soliton solutions to an integrable system of fifth-order nonlinear partial differential equations. By imposing some appropriate restrictions on the dependency constants, we show that those soliton solutions yield soliton solutions to the Sawada--Kotera equation. |
| title | Soliton solutions to the Sawada--Kotera equation |
| topic | Exactly Solvable and Integrable Systems 34A55 34M50 35C08 |
| url | https://arxiv.org/abs/2509.01009 |