New Exact Solutions to a Class of Fractional-Order Modified Unstable Schrödinger Equations

LIU Jingjing; SUN Yuhuai

doi:10.21656/1000-0887.420228

Volume 43 Issue 10

Oct. 2022

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LIU Jingjing, SUN Yuhuai. New Exact Solutions to a Class of Fractional-Order Modified Unstable Schrödinger Equations[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1185-1194. doi: 10.21656/1000-0887.420228

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New Exact Solutions to a Class of Fractional-Order Modified Unstable Schrödinger Equations

doi: 10.21656/1000-0887.420228

LIU Jingjing,
SUN Yuhuai^,

School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, P.R.China

Received Date: 2021-08-03
Rev Recd Date: 2021-09-06

Available Online: 2022-10-09

Publish Date: 2022-10-31

Abstract

Abstract

The fractional-order modified unstable Schrödinger equation (FMUSE) was studied, which describes the dispersion, nonlinearity, gain or absorption variation of optical pulses propagating in nonuniform fiber systems. First, the generalized fractional wave transform was appropriately used to convert the FMUSE into an ordinary differential equation, and the real and imaginary parts were separated and set as zero respectively, and the dispersion relation was obtained. By means of the modified (G'/G)-expansion method, a series of new exact analytical solutions with parameters were obtained, including trigonometric solutions, hyperbolic solutions and rational solutions, and the constraints ensuring the existence of solutions were given. Finally, the solutions of the dark solitary wave and the periodic wave were obtained with the parameters of special values.
- modified (G'/G)-expansion method,
- fractional-order modified unstable Schrödinger equation,
- exact solution

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References(16)

References

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