New types of exact solutions for the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation. (English) Zbl 1210.35241

Xu, Gui-Qiong

Appl. Math. Comput. 217, No. 12, 5967-5971 (2011).

Summary: We use two direct algebraic methods to solve a fourth-order dispersive cubic-quintic nonlinear Schrödinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain a new dark soliton and bright soliton, which may approach nonzero when the time variable approaches infinity. Then a series of analytical exact solutions are constructed by means of F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35Q51	Soliton equations
35C08	Soliton solutions
35A24	Methods of ordinary differential equations applied to PDEs
35B10	Periodic solutions to PDEs

Keywords:

nonlinear Schrödinger equation; soliton solution; periodic wave solution

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