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The nonlinear Schrödinger equation. Its interacting soliton equations and the inverse method

Interacting (Int) nonlinear Schrodinger (NLS) equations is a system of coupled nonlinear differential equations which is derived from the original NLS equation by an interacting soliton picture. By examining possible relations between a soliton solution u i which obeys the Int NLS equation and the solutions of the two-component equations which appear in the inverse method, we obtain the form of the natural Int NLS equations. We use only the knowledge of the forms of the equations concerned. The resulting form is different in several points from those of the other equations already treated i.e. the Korteweg-de Vries (KdV), sine-Gordon, modified KdV, Toda and Benjamin-Ono equations.