The (2+1)-dimensional hyperbolic nonlinear Schrödinger equation and its optical solitons

Dumitru Baleanu; Kamyar Hosseini; Soheil Salahshour; Khadijeh Sadri; Mohammad Mirzazadeh; Choonkil Park; Ali Ahmadian; Dumitru Baleanu; Kamyar Hosseini; Soheil Salahshour; Khadijeh Sadri; Mohammad Mirzazadeh; Choonkil Park; Ali Ahmadian

doi:10.3934/math.2021556

AIMS Mathematics

2021, Volume 6, Issue 9: 9568-9581. doi: 10.3934/math.2021556

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Research article

The (2+1)-dimensional hyperbolic nonlinear Schrödinger equation and its optical solitons

1.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey
2.
Institute of Space Sciences, Magurele-Bucharest, Romania
3.
Department of Medical Research, China Medical University, Taichung, 40447, Taiwan
4.
Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
5.
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
6.
Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157 Rudsar-Vajargah, Iran
7.
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, South Korea
8.
Institute of IR 4.0, The National University of Malaysia, 43600, Bangi, Selangor, Malaysia

Received: 28 March 2021 Accepted: 02 June 2021 Published: 25 June 2021
MSC : 35-XX, 35C08

A comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrödinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.
Citation: Dumitru Baleanu, Kamyar Hosseini, Soheil Salahshour, Khadijeh Sadri, Mohammad Mirzazadeh, Choonkil Park, Ali Ahmadian. The (2+1)-dimensional hyperbolic nonlinear Schrödinger equation and its optical solitons[J]. AIMS Mathematics, 2021, 6(9): 9568-9581. doi: 10.3934/math.2021556

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Abstract

A comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrödinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.

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