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

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.


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
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