Bright and dark soliton solutions for some nonlinear fractional differential equations

doi:10.1088/1674-1056/25/3/030203

中国物理B ›› 2016, Vol. 25 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/25/3/030203

Bright and dark soliton solutions for some nonlinear fractional differential equations

Ozkan Guner, Ahmet Bekir

1. Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri, Turkey;
2. Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir, Turkey

收稿日期:2015-09-19 修回日期:2015-10-25 出版日期:2016-03-05 发布日期:2016-03-05
通讯作者: Ozkan Guner, Ahmet Bekir E-mail:ozkanguner@karatekin.edu.tr;abekir@ogu.edu.tr

Bright and dark soliton solutions for some nonlinear fractional differential equations

Ozkan Guner¹, Ahmet Bekir²

1. Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri, Turkey;
2. Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir, Turkey

Received:2015-09-19 Revised:2015-10-25 Online:2016-03-05 Published:2016-03-05
Contact: Ozkan Guner, Ahmet Bekir E-mail:ozkanguner@karatekin.edu.tr;abekir@ogu.edu.tr

摘要/Abstract

摘要： In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona-Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann-Liouville sense.

关键词: exact solutions, ansatz method, space-time fractional modified Benjamin-Bona-Mahoney equation, time fractional mKdV equation

Abstract: In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona-Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann-Liouville sense.

Key words: exact solutions, ansatz method, space-time fractional modified Benjamin-Bona-Mahoney equation, time fractional mKdV equation

中图分类号: (Partial differential equations)

02.30.Jr

05.45.Yv (Solitons)

Ozkan Guner, Ahmet Bekir. Bright and dark soliton solutions for some nonlinear fractional differential equations[J]. 中国物理B, 2016, 25(3): 30203-030203.

Ozkan Guner, Ahmet Bekir. Bright and dark soliton solutions for some nonlinear fractional differential equations[J]. Chin. Phys. B, 2016, 25(3): 30203-030203.

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Bright and dark soliton solutions for some nonlinear fractional differential equations

Bright and dark soliton solutions for some nonlinear fractional differential equations

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