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Article Dans Une Revue Theoretical and Mathematical Physics Année : 2022

On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems

Résumé

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 the vector complex mKdV. This means that any common particular solution of both these two-dimensional integrable systems yields a corresponding particular solution of the three-dimensional Hirota-Ohta system. Using the Zakharov-Shabat dressing method, we derive the N-soliton solutions of these systems and analyze their interactions, i.e., explicitly derive 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 Hirota-Ohta-type system to these nonlinear evolution equations and obtain its N-soliton solutions.

Dates et versions

hal-03898791 , version 1 (14-12-2022)

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Citer

V. Gerdjikov, Nianhua Li, Vladimir Matveev, A. Smirnov. On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems. Theoretical and Mathematical Physics, 2022, 213 (1), pp.1331-1347. ⟨10.1134/S0040577922100038⟩. ⟨hal-03898791⟩
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