Mapping between nonlinear Schrödinger equations with real and complex potentials
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Publication:398231
zbMATH Open1300.35134arXiv1306.3643MaRDI QIDQ398231
Publication date: 12 August 2014
Published in: Journal of Geometry and Symmetry in Physics (Search for Journal in Brave)
Abstract: A mapping between stationary solutions of nonlinear Sch"odinger 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 the damped dynamics of a quantum harmonic oscillator and the case of dissipative periodic soliton solutions of the nonlinear Schr"odinger equation with complex potential.
Full work available at URL: https://arxiv.org/abs/1306.3643
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)
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