New exact solutions to the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. (English) Zbl 1195.35283

Zhang, Zai-Yun; Liu, Zhen-Hai; Miao, Xiu-Jin; Chen, Yue-Zhong

Appl. Math. Comput. 216, No. 10, 3064-3072 (2010).

Summary: By using the modified mapping method and the extended mapping method, we derive some new exact solutions of the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity, which are the linear combination of two different Jacobi elliptic functions and we also consider the solutions in the limit cases.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35A24	Methods of ordinary differential equations applied to PDEs

Keywords:

perturbed nonlinear Schrödinger’s equation; exact solutions; modified mapping method; extended mapping method; Kerr law nonlinearity

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