Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

doi:10.1088/1674-1056/abd165

中国物理B ›› 2021, Vol. 30 ›› Issue (5): 50202-050202.doi: 10.1088/1674-1056/abd165

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

Zillur Rahman^1,2, M Zulfikar Ali², and Harun-Or Roshid^3,†

1 Department of Mathematics, Comilla University, Cumilla-3506, Bangladesh;
2 Department of Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh;
3 Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh

收稿日期:2020-10-06 修回日期:2020-11-28 接受日期:2020-12-08 出版日期:2021-05-14 发布日期:2021-05-14
通讯作者: Harun-Or Roshid E-mail:harunorroshidmd@gmail.com

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

Zillur Rahman^1,2, M Zulfikar Ali², and Harun-Or Roshid^3,?

1 Department of Mathematics, Comilla University, Cumilla-3506, Bangladesh;
2 Department of Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh;
3 Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh

Received:2020-10-06 Revised:2020-11-28 Accepted:2020-12-08 Online:2021-05-14 Published:2021-05-14
Contact: Harun-Or Roshid E-mail:harunorroshidmd@gmail.com

摘要/Abstract

摘要： We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model. Specifically, we apply the approach to the nonlinear space-time fractional model leading the wave to spread in electrical transmission lines (s-tfETL), the time fractional complex Schrödinger (tfcS), and the space-time M-fractional Schrödinger-Hirota (s-tM-fSH) models to verify the effectiveness of the proposed approach. The implementing of the introduced new technique based on the models provides us with periodic envelope, exponentially changeable soliton envelope, rational rogue wave, periodic rogue wave, combo periodic-soliton, and combo rational-soliton solutions, which are much interesting phenomena in nonlinear sciences. Thus the results disclose that the proposed technique is very effective and straight-forward, and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.

关键词: improved Kudryashov method, fractional electrical transmission line equation, fractional nonlinear complex Schrö, dinger equation, M-fractional Schrö, dinger-Hirota (s-tM-fSH)

Abstract: We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model. Specifically, we apply the approach to the nonlinear space-time fractional model leading the wave to spread in electrical transmission lines (s-tfETL), the time fractional complex Schrödinger (tfcS), and the space-time M-fractional Schrödinger-Hirota (s-tM-fSH) models to verify the effectiveness of the proposed approach. The implementing of the introduced new technique based on the models provides us with periodic envelope, exponentially changeable soliton envelope, rational rogue wave, periodic rogue wave, combo periodic-soliton, and combo rational-soliton solutions, which are much interesting phenomena in nonlinear sciences. Thus the results disclose that the proposed technique is very effective and straight-forward, and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.

Key words: improved Kudryashov method, fractional electrical transmission line equation, fractional nonlinear complex Schrö, dinger equation, M-fractional Schrö, dinger-Hirota (s-tM-fSH)

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems) 04.20.Jb (Exact solutions) 05.45.Yv (Solitons)

Zillur Rahman, M Zulfikar Ali, and Harun-Or Roshid. Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method[J]. 中国物理B, 2021, 30(5): 50202-050202.

Zillur Rahman, M Zulfikar Ali, and Harun-Or Roshid. Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method[J]. Chin. Phys. B, 2021, 30(5): 50202-050202.

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Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

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