The conditions for the existence of a Lax pair were determined and exact analytic solutions to the nonlinear evolution equations of the Schrödinger type with complex and nonuniform potentials were found. In particular, these solutions provide a basis for the soliton management concept in applied problems and solve the problems of optimal energy accumulation by a Schrödinger soliton in an active medium and soliton amplification in optical fiber communication lines and soliton lasers.
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Serkin et al. (2001) studied this question.
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