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Bifurcation, similarity reduction, conservation laws and exact solutions of modified-Korteweg-de Vries–Burger equation

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Abstract

In this paper, non-linear propagation of oscillatory and monotonous DIA shocks in dusty plasma with dust charge fluctuations and small isothermal deviation of electrons is considered. The modified-Korteweg-de Vries–Burger (m-KdVB) equation can be derived by using the reductive perturbation (R-P) method. The variational principle and the conservation laws of the m-KdVB equation are constructed by introducing two special functions. A nonlinear self-adjoint classification of the m-KdVB equation is presented. Based on the Ibragimov’s theorem, conservation laws for m-KdVB equation are established. We also study the m-KdVB equations by improved \(\tan \left( \frac{\psi (\chi )}{2}\right) \)-expansion method. Abundant dark, singular and periodic optical solitons solutions of the model are constructed. Furthermore, additional graphical simulations were performed using mathematica to see the behavior of these solutions. With the help of bifurcation theory of planar dynamical systems, we study bifurcation and phase portrait analysis of traveling wave solution of the m-KdVB equation.

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Authors and Affiliations

  1. Faculty of Computers and Artificial Intelligence, Cairo University, Dr. Ahmed Zewail St. 5, Giza, 12613, Egypt

    Shrouk Wael

  2. Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt

    Engy. A. Ahmed & Rafat S. Ibrahim

  3. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, 41411, Medina, Kingdom of Saudi Arabia

    Aly R. Seadawy

  4. Department of Mathematics, Faculty of Science and Arts in Baljurashi, Al-Baha University, Al-Baha, Kingdom of Saudi Arabia

    Rafat S. Ibrahim

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  1. Shrouk Wael
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  2. Engy. A. Ahmed
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Correspondence to Aly R. Seadawy.

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Wael, S., Ahmed, E.A., Seadawy, A.R. et al. Bifurcation, similarity reduction, conservation laws and exact solutions of modified-Korteweg-de Vries–Burger equation. Opt Quant Electron 55, 262 (2023). https://doi.org/10.1007/s11082-022-04517-7

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