A comparative analysis of Painleve, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schrodinger equations

作者：Al Khawaja U^*

来源：Journal of Mathematical Physics, 2010, 51(5): 053506.

DOI：10.1063/1.3397534

We derive the integrability conditions of nonautonomous nonlinear Schrodinger equations using the Lax pair and similarity transformation methods. We present a comparative analysis of these integrability conditions with those of the Painleve method. We show that while the Painleve integrability conditions restrict the dispersion, nonlinearity, and dissipation/gain coefficients to be space independent and the external potential to be only a quadratic function of position, the Lax Pair and the similarity transformation methods allow for space-dependent coefficients and an external potential that is not restricted to the quadratic form. The integrability conditions of the Painleve method are retrieved as a special case of our general integrability conditions. We also derive the integrability conditions of nonautonomous nonlinear Schrodinger equations for two-and three-spacial dimensions.

• 出版日期2010-5