Painlevé Analysis for (2 + 1) Dimensional Non-Linear Schr?dinger Equation

摘要

style="text-align:justify;"> This paper investigates a real version of a (2 + 1) dimensional nonlinear Schr style="color:#454545;font-family:Simsun;font-size:14px;white-space:normal;background-color:#FFFFFF;">ödinger equation through adoption of Painlevé test by means of which the (2 + 1) dimensional nonlinear Schr style="color:#454545;font-family:Simsun;font-size:14px;white-space:normal;background-color:#FFFFFF;">ödinger equation is studied according to the Weiss et al. method and Kruskal’s simplification algorithms. According to Painlevé test, it is found that the number of arbitrary functions required for explaining the Cauchy-Kovalevskaya theorem exist. Finally, the associated B style="color:#454545;font-family:Simsun;font-size:14px;white-space:normal;background-color:#FFFFFF;">äcklund transformation and bilinear form is directly obtained from the Painlevé test.