Abstract
The purpose of this paper is to investigate a higher-order nonlinear Schrödinger equation with non-Kerr term by using the bifurcation theory method of dynamical systems and to provide its bounded traveling wave solutions. Applying the theory, we discuss the bifurcation of phase portraits and investigate the relation between the bounded orbit of the traveling wave system and the energy level. Through the research, new traveling wave solutions are given, which include solitary wave solutions, kink wave solutions, and periodic wave solutions.
Highlights
In the past decades, communication systems have scored a great growth of the transmission capacity
The purpose of this paper is to investigate a higher-order nonlinear Schrodinger equation with non-Kerr term by using the bifurcation theory method of dynamical systems and to provide its bounded traveling wave solutions
Communication systems have scored a great growth of the transmission capacity
Summary
Communication systems have scored a great growth of the transmission capacity. When short pulses are considered, the equation can no longer represent the propagations of light pulses in fibers because higher-order dispersion terms and the non-Kerr nonlinearity effects cannot be neglected. Α2 should be an imaginary number, but many analytical studies have been done when α2 is real, such as Painleveproperty [5], inverse scattering transform [6], Hirota direct method, and conservation laws [7] These researches verify its integrable nature and have obtained many exact wave solutions. With the aid of Mathematica, we study the new traveling wave solutions for a higher-order NLS equation that contains the non-Kerr nonlinear terms, which describes propagation of very short pulses in highly nonlinear optical fibers by using different elliptic functions. Note that the existence of solitary wave solutions depends essentially on the model coefficients and on the specific nonlinear features of the medium
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