Chinese Journal of Quantum Electronics ›› 2019, Vol. 36 ›› Issue (4): 416-422.

• Quantum Physics • Previous Articles     Next Articles

The new exact solutions of cubic nonlinear schr\"{o}dinger equations

MA Zhi-min 1,*, SUN Yu-huai 2   

  1. 1 Department of Basic Courses,Engineering and Technical College of Chengdu University of Technology,Leshan,614000, China; 2 College of Mathematics and Software Science,Sichuan Normal University,Chengdu,610066,China
  • Received:2018-12-03 Revised:2019-01-06 Published:2019-07-28 Online:2019-07-11

Abstract: Constructing exact solutions of cubic nonlinear schr\"{o}dinger equation will be better help us to understand the physical phenomenon of cubic schr\"{o}dinger equation. Generalized exp(-\phi(\xi))-expansion method is given here. Based on this method and the aid of symbolic computation system-Maple,new exact solutions of cubic nonlinear schr\"{o}dinger equation are obtained. These solutions include hyperbolic function solutions, trigonometric function solutions and rational function solutions.As a result, many new exact solutions are obtained. New solutions can be used in optical communications. It has been shown that this method provides a powerful mathematical tool for solving nonlinear partial differential equations in mathematical physics problems.

Key words: nonlinear equations, exact solutions, generalized -expansion method, cubic nonlinear schrödinger equations, optical communications, symbolic computation

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