Elliptic function solutions, modulation instability and optical solitons analysis of the paraxial wave dynamical model w
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Elliptic function solutions, modulation instability and optical solitons analysis of the paraxial wave dynamical model with Kerr media Muhammad Arshad1 · Aly R. Seadawy2 · Dianchen Lu1 · Muhammad Shoaib Saleem3 Received: 12 June 2020 / Accepted: 20 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The optical solitary waves explain non-dispersive and non-diffractive spatiotemporal localized waves envelopes promulgating in the media of optical Kerr. These propagations are generally described by the nonlinear Schrö dinger equation. The modified extended mapping technique is utilized to assemble the solitons, solitary waves and rational solutions of time-dependent dimensionless paraxial wave equation. The obtained different sorts of wave solutions encompass key applications in physics and engineering. By giving appropriate values to parameter, special sorts of solitary waves configuration can be displayed graphically. The physical interpretation of the solution can be understood through the structure. The stability of this wave equation is investigated via using modulational instability analysis which authenticates that all soliton solutions are stable and exact. Several analytical results and working out have confirmed the strength and efficacy of the current technique. Keywords Modified extended mapping method · Paraxial wave model · Solitons · Solitary waves solutions · Periodic solutions
1 Introduction Nonlinear partial differential equation (NLPDEs) often appears in the basic laws of nature. In the areas of mthematical physics and other applied sciences, various models naturally arise from plasma physics, solid state physics, ocean and atmospheric waves, hydrodynamics, chemistry, biology, mathematical materials sciences, etc (Agrawal 2013; Zakharov 1972; Arshad et al. 2017a, b; Seadawy et al. 2018; Najafi and Arbabi 2014; Arshad and Seadawy 2017; Triki and Biswas 2011; Zhang and Si 2010). The promulgation of * Aly R. Seadawy [email protected] Muhammad Arshad [email protected] 1
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, People’s Republic of China
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Mathematics Department, Faculty of Science, Taibah University, Medina, Saudi Arabia
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Department of Mathematics, University of Okara, Okara, Pakistan
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non-linear wave is one of the most significant phenomena naturally, and more and more concentration has been paid to the investigation of nonlinear wave dynamic system. To understand the qualitative distinctiveness of diverse phenomena, the analytical results of NLPDEs contribute a key role correctly. Due to the analytical solution of NLPDEs, the mechanism of numerous nonlinear and complex phenomena’s are identified by graphics and symbolically, such as diversity beneath dissimilar circumstances or steady-state diversity, spatial positioning procedure of transmission, existence of peak organism, etc. There are several unknown parameters and variables in the majority
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