Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schr\"odinger equations
Exactly Solvable and Integrable Systems
2017-07-25 v1
Abstract
A bilinearisation-reduction approach is described for finding solutions for nonlocal integrable systems and is illustrated with nonlocal discrete nonlinear Schr\"odinger equations. In this approach we first bilinearise the coupled system before reduction and derive its double Casoratian solutions, then we impose reduction on double Casoratians so that they coincide with the nonlocal reduction on potentials. Double Caosratian solutions of the classical and nonlocal (reverse space, reverse time and reverse space-time) discrete nonlinear Schr\"odinger equations are presented.
Keywords
Cite
@article{arxiv.1707.07253,
title = {Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schr\"odinger equations},
author = {Xiao Deng and Senyue Lou and Da-jun Zhang},
journal= {arXiv preprint arXiv:1707.07253},
year = {2017}
}
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8 pages