Abstract
We derive the Lax pairs and integrability conditions of the nonlinear Schrödinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrödinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrödinger equation.
Original language | English |
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Pages (from-to) | 171-178 |
Number of pages | 8 |
Journal | Communications in Theoretical Physics |
Volume | 66 |
Issue number | 2 |
DOIs | |
Publication status | Published - Aug 1 2016 |
Keywords
- Lax pair
- exact solutions
- integrability
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)