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This article is cited in 3 scientific papers (total in 3 papers)
On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems
V. S. Gerdjikovab, Nianhua Lic, V. B. Matveevde, A. O. Smirnovf a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
b Institute for Advanced Physical Studies, Sofia, Bulgaria
c School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, China
d Institut de Mathématiques de Bourgogne (IMB),
Dijon, France
e St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
f Saint-Petersburg State University of Aerospace Instrumentation
Abstract:
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.
Keywords:
two-dimensional Kulish–Sklyanin system, three-dimensional Hirota–Ohta system, Lax representation, dressing method, multisoliton solutions, two-dimensional reductions.
Received: 05.02.2022 Revised: 05.02.2022
Citation:
V. S. Gerdjikov, Nianhua Li, V. B. Matveev, A. O. Smirnov, “On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems”, TMF, 213:1 (2022), 20–40; Theoret. and Math. Phys., 213:1 (2022), 1331–1347
Linking options:
https://www.mathnet.ru/eng/tmf10267https://doi.org/10.4213/tmf10267 https://www.mathnet.ru/eng/tmf/v213/i1/p20
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