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An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients

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  • Osman, M.S.
  • Wazwaz, Abdul-Majid

Abstract

Herein, we present an efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional Korteweg–de Vries equation with time-dependent coefficients. We employ the generalized unified method, which presents a wider applicability for handling many other nonlinear evolution equations in different branches of science, to find these solutions. The dynamical behavior of the traveling wave solutions and their structures are discussed by different choices for the arbitrary functions in the obtained solutions.

Suggested Citation

  • Osman, M.S. & Wazwaz, Abdul-Majid, 2018. "An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 282-289.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:282-289
    DOI: 10.1016/j.amc.2017.10.042
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    References listed on IDEAS

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    1. Yong Chen, 2005. "A New General Algebraic Method With Symbolic Computation To Construct New Traveling Solution For The(1 +1)-Dimensional Dispersive Long Wave Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1107-1119.
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    Cited by:

    1. Rizvi, Syed Tahir Raza & Khan, Salah Ud-Din & Hassan, Mohsan & Fatima, Ishrat & Khan, Shahab Ud-Din, 2021. "Stable propagation of optical solitons for nonlinear Schrödinger equation with dispersion and self phase modulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 126-136.
    2. Christodoulos Sophocleous, 2024. "Lie Group Classification of a Class of Variable Coefficient Boiti–Leon–Manna–Pempinelli Equations," Mathematics, MDPI, vol. 12(22), pages 1-13, November.
    3. Ali, Ahmad T. & Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Lu, Dianchen, 2020. "Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Lu, D. & Osman, M.S. & Khater, M.M.A. & Attia, R.A.M. & Baleanu, D., 2020. "Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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