Soliton Solutions of the Derivative Nonlinear Schrödinger Equation

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Abstract
By using the inverse scattering method the soliton solutions are examined analytically and numerically under both (I) vanishing and (II) nonvanishing conditions. The two-soliton solution for (I) shows that two solitons collide as if they were particles. For the case (II) there appears a “paired soliton” which generally pulsates with a period (“pulsative soliton”) but degenerates to a stationary one (“pure soliton”) in a limited case. There exist two types of pure solitons, envelope bright and dark solitons, between which some cases of collisions are examined. The collision between solitons of same types is similar to that of (I), while the other collisions are different from the previous case.