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Symbolic computation to construct new soliton solutions and dynamical behaviors of various wave structures for two different extended and generalized nonlinear Schrödinger equations using the new improved modified generalized sub-ODE proposed method

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  • El-Ganaini, Shoukry
  • Kumar, Sachin

Abstract

In this work, we propose a new improved modified generalized sub-ODE method for constructing new solitons and traveling wave solutions, and also show the dynamical behaviors of various wave structures to the extended nonlinear Schrödinger equation with higher-order odd and even terms, as well as a generalized nonlinear Schrödinger equation of fourth-order, using symbolic computerized work via Mathematica. This newly proposed method improves and modifies the Li method (Li-Hua and Jin-Yu, 2009) The improved method presented in this paper can be used to solve other nonlinear equations with nonlinear terms of any order of physical systems in order to obtain many solitary wave solutions and other traveling wave solutions for such nonlinear models in a unified manner. The resulting soliton solutions and other forms of solutions are very useful and advantageous in many branches of mathematical physics and nonlinear sciences such as ocean engineering, optical fibers, plasma physics, and fluid dynamics.

Suggested Citation

  • El-Ganaini, Shoukry & Kumar, Sachin, 2023. "Symbolic computation to construct new soliton solutions and dynamical behaviors of various wave structures for two different extended and generalized nonlinear Schrödinger equations using the new impr," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 28-56.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:28-56
    DOI: 10.1016/j.matcom.2023.01.013
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    References listed on IDEAS

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    1. El-Ganaini, Shoukry & Kumar, Hitender, 2020. "A variety of new traveling and localized solitary wave solutions of a nonlinear model describing the nonlinear low- pass electrical transmission lines," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Chen, Yong & Yan, Zhenya, 2006. "The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 948-964.
    3. Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    4. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    5. Kumar, Sachin & Dhiman, Shubham Kumar & Chauhan, Astha, 2022. "Symmetry reductions, generalized solutions and dynamics of wave profiles for the (2+1)-dimensional system of Broer–Kaup–Kupershmidt (BKK) equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 319-335.
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