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

• Published in: Theoretical and mathematical physics Vol. 213; no. 1; pp. 1331 - 1347
• Main Authors: Gerdjikov, V. S., Li, Nianhua, Matveev, V. B., Smirnov, A. O.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.10.2022; Springer Nature B.V; Consultants bureau
• Subjects: 14/34; 639/766/189; 639/766/530; 639/766/747; Applications of Mathematics; Eigenvalues; Linear equations; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Nonlinear evolution equations; Physics; Physics and Astronomy; Solitary waves; Theoretical; two-dimensional Kulish–Sklyanin system; two-dimensional reductions; Lax representation; three-dimensional Hirota–Ohta system; dressing method; multisoliton solutions; two-dimensional Kulish-Sklyanin system; three-dimensional Hirota-Ohta system
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S0040577922100038

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 -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 -soliton solutions.