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N-Fold Darboux Transformation for the Nonlocal Nonlinear Schrödinger (NNLS) Equation with the Self-Induced PT-Symmetric Potential

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Document pages: 13 pages

Abstract: The Darboux transformation (DT) method is studied ina lot of local equations, but there are few of work to solve nonlocal equationsby DT. In this letter, we solve the nonlocal nonlinear Schrödinger equation (NNLSE) with the self-induced PT-symmetric potential by DT. Thenthe N-fold DT of NNLSE is derived with the help of the gauge transformationbetween the Lax pairs. Then we derive some novel exact solutions including thebright soliton, breather wave soliton. In particularly, the dynamic features ofone-soliton, two-soliton, three-soliton solutions and the elastic interactionsbetween the two solitons are displayed.

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