On optical soliton solutions of new Hamiltonian amplitude equation via Jacobi elliptic functions
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On optical soliton solutions of new Hamiltonian amplitude equation via Jacobi elliptic functions Asim Zafar1, M. Raheel2 , Khalid K. Ali3,a
, Waseem Razzaq2
1 Department of Mathematics, CUI, Vehari Campus, Vehari, Pakistan 2 Department of Mathematics and Statistics, ISP Multan, Multan, Pakistan 3 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
Received: 21 May 2020 / Accepted: 13 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this article, the extended Jacobi elliptic expansion function scheme is applied to obtain the optical soliton solutions of the new Hamiltonian amplitude equation. The obtained traveling wave solutions are verified through MATHEMATICA. In the end, the graphs are also drawn from the solutions. These optical soliton solutions show that the suggested scheme is effective, reliable and simple as compared to many other schemes.
1 Introduction The theory of optical solitons is one of the pleasurable topics for the investigation of solitons propagation through nonlinear optical fibers, intense laser radiation into plasmas [1–4]. Soliton solutions remit motivation to do work in the disparate fields of consisting spectroscopy, photonic and optical fibers. A large number of models that are impressive illustrate the enterprising of solitons assistance, see, for example, [5–15]. Mostly naturally occurring phenomena are modeled in the structure of nonlinear Schrödinger equations (NLSEs) [16–18]. Different types of schemes have been applied to obtain the optical soliton solutions of the new Hamiltonian amplitude equation. For example, solitary wave solutions of new Hamiltonian amplitude equation have been found by using the Jacobi elliptic function scheme [19]. Exact solitons of the new Hamiltonian amplitude equation are determined by applying the Riccti equation technique [20]. The first integral scheme is a scheme that is applicable both for integrable and non-integrable equations. By using this scheme, exact soliton solutions of the new Hamiltonian amplitude equation are determined [21]. Periodic and hyperbolic soliton solutions of the nonlinear Schrödinger naming new Hamiltonian amplitude equation have been determined by using the functional variable scheme [22]. Different types of soliton solutions of the new Hamiltonian amplitude equation are determined by applying the Lie classical scheme and ( GG )-expansion method [23]. Exact soliton solution of new Hamiltonian amplitude equation is determined by using the two different techniques, He’s semi-inverse scheme and the anstaz scheme [24]. Exact periodic soliton solutions and some other solutions
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
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of new Hamiltonian amplitude equation are found by applying the modified simple equation technique [25]. There is a very useful and helpful scheme, naming extended Jacobi elliptic function expansion s
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