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Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation

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  • Sil, Subhankar
  • Raja Sekhar, T.
  • Zeidan, Dia

Abstract

We compute nonlocal symmetries and obtain kink type soliton solutions to an integrable soliton equation. We construct a tree of nonlocally related partial differential equations (PDEs) of integrable soliton equation which consists of potential systems arising from conservation laws based method and inverse potential systems (IPS) from symmetry based method. We show that the integrable soliton equation admits two nonlocal symmetries among these one of which results from potential system and the other from locally related subsystem of IPS. We propose a systematic procedure to obtain exact solutions of a given PDE system using nonlocal symmetry which arises from IPS or its locally related subsystem. Finally, we obtain exact solutions to integrable soliton equation using nonlocal symmetries and discuss the physical behavior of the explicit solution graphically.

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  • Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304082
    DOI: 10.1016/j.chaos.2020.110010
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    1. Du, Xia-Xia & Tian, Bo & Qu, Qi-Xing & Yuan, Yu-Qiang & Zhao, Xue-Hui, 2020. "Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
    3. Satapathy, Purnima & Raja Sekhar, T., 2018. "Optimal system, invariant solutions and evolution of weak discontinuity for isentropic drift flux model," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 107-116.
    4. Bansal, Anupma & Kara, A.H. & Biswas, Anjan & Moshokoa, Seithuti P. & Belic, Milivoj, 2018. "Optical soliton perturbation, group invariants and conservation laws of perturbed Fokas–Lenells equation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 275-280.
    5. Wang, Gangwei & Kara, Abdul H. & Fakhar, Kamran & Vega-Guzman, Jose & Biswas, Anjan, 2016. "Group analysis, exact solutions and conservation laws of a generalized fifth order KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 8-15.
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    Cited by:

    1. Sil, Subhankar & Raja Sekhar, T., 2023. "Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    2. Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Vijay Anand, R. & Dinakaran, M. & Balusamy, Balamurugan & Gao, Wei, 2021. "Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 566-602.
    3. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Mandal, Sougata & Sil, Subhankar & Ghosh, Sukhendu, 2024. "Lie symmetries and optimal classifications with certain modal approaches for the three-dimensional gas-dynamical equations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Manjit Singh & Shou-Fu Tian, 2023. "Lie symmetries, group classification and conserved quantities of dispersionless Manakov–Santini system in (2+1)-dimension," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 312-329, June.
    6. Karna, Ashutosh Kumar & Satapathy, Purnima, 2023. "Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Shagolshem, Sumanta & Bira, B. & Zeidan, D., 2023. "Optimal subalgebras and conservation laws with exact solutions for biological population model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    8. Shagolshem, Sumanta & Bira, B. & Sil, Subhankar, 2022. "Conservation laws and some new exact solutions for traffic flow model via symmetry analysis," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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