Abstract
The generalized dressing method is extended to variable-coefficient AKNS equations, including a variable-coefficient coupled nonlinear Schrödinger equation and a variable-coefficient coupled mKdV equation. A general variable-coefficient KP equation is proposed and decomposed into the two 1+1 dimensional variable-coefficient soliton equations. As applications, we obtain exact solutions of these variable-coefficient soliton equations in 1+1- and 2+1- dimensions.
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