Geodesic
On soliton solutions and soliton interactions of Kulish--Sklyanin and Hirota--Ohta systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 20-40

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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, two-dimensional reductions.
Mots-clés : multisoliton solutions 
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     author = {V. S. Gerdjikov and Nianhua Li and V. B. Matveev and A. O. Smirnov},
     title = {On soliton solutions and soliton interactions of {Kulish--Sklyanin} and {Hirota--Ohta} systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a1/}
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V. S. Gerdjikov; Nianhua Li; V. B. Matveev; A. O. Smirnov. On soliton solutions and soliton interactions of Kulish--Sklyanin and Hirota--Ohta systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 20-40. http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a1/