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The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows

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  • Seadawy, Aly R.
  • Arshad, Muhammad
  • Lu, Dianchen

Abstract

In this paper, the weakly nonlinear wave propagation theory in the occurrence of magnetic fields in fluids of superposed is studied. The amplitude evolution of governing equations of the amplitude of the progressive waves is reported. The soliton and other kinds solutions of (2+1)-dimensional elliptic nonlinear Schrödinger equation is constructed. We also investigate the properties of envelope of the (2+1)-dimensional wave pocket. The propagation of pulses ahead of ultra-short range in the optical communication systems is illustrated by this dynamical equation. The modified and extended rational expansion method is utilized for obtaining different kinds of wave solutions such as bright-dark solitons, solitons of Kink and anti-Kink, solitary waves, periodic solutions and elliptic function solutions of this equation. These achieved exact solutions are further general and useful to researcher for understanding physical phenomena. Several solutions are novel by comparing these solutions with existing solutions. The power and effectiveness of current can observed form constructed solutions.

Suggested Citation

  • Seadawy, Aly R. & Arshad, Muhammad & Lu, Dianchen, 2020. "The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920305373
    DOI: 10.1016/j.chaos.2020.110141
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    References listed on IDEAS

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    1. Seadawy, Aly R. & Nasreen, Naila & Lu, Dianchen & Arshad, Muhammad, 2020. "Arising wave propagation in nonlinear media for the (2+1)-dimensional Heisenberg ferromagnetic spin chain dynamical model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Seadawy, Aly R., 2015. "Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 124-131.
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    Cited by:

    1. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z. & Qasim, Muhammad, 2022. "Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Ullah, Mohammad Safi & Baleanu, Dumitru & Ali, M. Zulfikar & Harun-Or-Roshid,, 2023. "Novel dynamics of the Zoomeron model via different analytical methods," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Bashir, Azhar & Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R., 2022. "The Weierstrass and Jacobi elliptic solutions along with multiwave, homoclinic breather, kink-periodic-cross rational and other solitary wave solutions to Fornberg Whitham equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z., 2022. "Demonstration of unique problems from Soliton solutions to nonlinear Selkov–Schnakenberg system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Seadawy, Aly R. & Rizvi, Syed T.R. & Sohail, Muhammad & Ali, Kashif, 2022. "Nonlinear model under anomalous dispersion regime: Chirped periodic and solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    6. Farman, Muhammad & Sarwar, Rabia & Akgul, Ali, 2023. "Modeling and analysis of sustainable approach for dynamics of infections in plant virus with fractal fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Khan, Kashif Ali & Seadawy, Aly R. & Raza, Nauman, 2022. "The homotopy simulation of MHD time dependent three dimensional shear thinning fluid flow over a stretching plate," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    8. Seadawy, Aly R. & Ali, Safdar & Rizvi, Syed T.R., 2022. "On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    9. Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R. & Ali, Kashif, 2022. "Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    10. Rubayyi T. Alqahtani & Melike Kaplan, 2024. "Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation," Mathematics, MDPI, vol. 12(5), pages 1-10, February.

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