Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative

YANG Na; CHEN Longwei; XIONG Mei

doi:10.21656/1000-0887.380302

Volume 39 Issue 10

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YANG Na, CHEN Longwei, XIONG Mei. Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302

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Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative

doi: 10.21656/1000-0887.380302

School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, P.R.China

Funds: The National Natural Science Foundation of China(11761075)

Received Date: 2017-12-05
Rev Recd Date: 2018-01-17
Publish Date: 2018-10-01

Abstract

Abstract

With the dynamic system method, the qualitative performance and the exact solution of the general nonlinear Schr?dinger equation with derivative were studied. Through the traveling wave transformation, the corresponding ordinary differential equation was deduced and the first integral was calculated. Under different parameter space conditions, the bifurcations of the general nonlinear Schrödinger equation with derivative were investigated, and the exact traveling wave solutions were obtained, such as solitary solutions, periodic solutions as well as kink and anti-kink solutions. The solitary wave solutions were considered through numerical simulation. The results show that the present findings improve the related previous conclusions.
- nonlinear Schr?dinger equation,
- dynamic system,
- solitary wave solution

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References

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