On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems
| Autor: | Gerdjikov, Vladimir S., Li, Nianhua, Matveev, Vladimir B., Smirnov, Alexandr O. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S0040577922100038 |
| Popis: | In this paper we consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota-Ohta system. The Lax pair of the Hirota-Ohta system was extended to a Lax triad by adding extra third linear equation, whose compatibility conditions with the Lax pair of the Hirota-Ohta imply another remarkable systems: the Kulish-Sklyanin system (KSS) together with its first higher commuting flow, which we can call as vector complex MKdV. This means that any common particular solution of these both two-dimensional integrable systems yields a corresponding particular solution of the three-dimensional Hirota-Ohta system. Using the dressing Zakharov-Shabat method we derive the $N$-soliton solutions of these systems and analyze their interactions, i.e. derive explicitly the shifts of the relative center-of-mass coordinates and the phases as functions of the discrete eigenvalues of the Lax operator. Next we relate to these NLEE system of Hirota--Ohta type and obtain its $N$-soliton solutions Comment: 17 pages; several new references added |
| Databáze: | arXiv |
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