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Mapping between nonlinear Schrödinger equations with real and complex potentials. (English) Zbl 1300.35134

Summary: A mapping between the stationary solutions of nonlinear Schrödinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific examples we consider the case of dissipative periodic soliton solutions of the nonlinear Schrödinger equation with complex potential.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35Q41 Time-dependent Schrödinger equations and Dirac equations
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