Stability for line soliton to the Davey-Stewartson I equation

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[Abstract] Resonance phenomena exist in interaction between the line soliton and the periodic soliton expressed by Davey-Stewartson (DS) equation. If resonant conditions are completely satisfied, two solitons become resonant line soliton after collision and continue propagating. However, considering interaction of the line soliton and the periodic soliton having parameters of the vicinity of the parameters that satisfy resonant conditions, a quasi resonant state can be constituted by having the line soliton and periodic soliton collide. This quasi resonant state can be seen as a state that minute disturbance is added to the line soliton. The exact solution which expresses this quasi resonant state expresses time evolution of the line soliton and disturbance at the time when minute disturbance is added to the line soliton.

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