On Tzitéeica type nonlinear equations for multiple soliton solutions in nonlinear optics

Yongsheng Rao; Asim Zafar; Alper Korkmaz; Asfand Fahad; Muhammad Imran Qureshi; Yongsheng Rao; Asim Zafar; Alper Korkmaz; Asfand Fahad; Muhammad Imran Qureshi

doi:10.3934/math.2020423

AIMS Mathematics

2020, Volume 5, Issue 6: 6580-6593. doi: 10.3934/math.2020423

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On Tzitéeica type nonlinear equations for multiple soliton solutions in nonlinear optics

1.
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 511400, China
2.
Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan
3.
The IJEMAPS Journal 99427 Weimar, Thuringen, Germany

Received: 05 July 2020 Accepted: 17 August 2020 Published: 24 August 2020
MSC : 35A09

Nonlinear equations personate a consequential role in scientific fields such as nonlinear optics, solid state physics and quantum field theory. This article studies the Tzitzéica-Dodd-Bullough-Mikhailov and Tzitzéica-type equations that appear in nonlinear optics. The Painlevé and traveling wave transformations both play a key role in revamping the aforementioned equations into nonlinear ordinary differential equations. Then, the simple ansatz approach is followed to seize complex singular, complex bright solitons and other kink type solutions. The existing literature unveils that this study is a novel contribution in the literature and the proposed approach is forthright and simple to implement for solving nonlinear problems. This approach has no extra condition as compared to many other techniques have. We also verify and interpret graphically the secured solutions through symbolic software Mathematica and MatLab respectively.
- nonlinear equations,
- simple ansatz approach,
- soliton solutions
Citation: Yongsheng Rao, Asim Zafar, Alper Korkmaz, Asfand Fahad, Muhammad Imran Qureshi. On Tzitéeica type nonlinear equations for multiple soliton solutions in nonlinear optics[J]. AIMS Mathematics, 2020, 5(6): 6580-6593. doi: 10.3934/math.2020423

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Abstract

Nonlinear equations personate a consequential role in scientific fields such as nonlinear optics, solid state physics and quantum field theory. This article studies the Tzitzéica-Dodd-Bullough-Mikhailov and Tzitzéica-type equations that appear in nonlinear optics. The Painlevé and traveling wave transformations both play a key role in revamping the aforementioned equations into nonlinear ordinary differential equations. Then, the simple ansatz approach is followed to seize complex singular, complex bright solitons and other kink type solutions. The existing literature unveils that this study is a novel contribution in the literature and the proposed approach is forthright and simple to implement for solving nonlinear problems. This approach has no extra condition as compared to many other techniques have. We also verify and interpret graphically the secured solutions through symbolic software Mathematica and MatLab respectively.

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