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

We consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota–Ohta system. The Lax pair system was extended to triad by adding extra third linear equation, whose compatibility conditions with imply another systems: Kulish–Sklyanin (KSS) together its first higher commuting flow, which we can call vector complex mKdV. This means that any common particular solution both these integrable systems yields corresponding Using Zakharov–Shabat dressing method, derive $$N$$ -soliton solutions and analyze their interactions, i.e., explicitly shifts relative center-of-mass coordinates phases as functions discrete eigenvalues operator. Next, relate Hirota–Ohta-type nonlinear evolution equations obtain solutions.