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Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations

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  • Wazwaz, Abdul-Majid

Abstract

The nonlinear Klein–Gordon equations with power law nonlinearities are studied. The tanh method is used for analytic treatment for these equations. The analysis leads to travelling wave solutions with compactons, solitons, solitary patterns and periodic structures.

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  • Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:1005-1013
    DOI: 10.1016/j.chaos.2005.08.145
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    References listed on IDEAS

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    1. Wazwaz, A.M., 2001. "A study of nonlinear dispersive equations with solitary-wave solutions having compact support," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(3), pages 269-276.
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    Cited by:

    1. Bekir, Ahmet, 2009. "The tanh–coth method combined with the Riccati equation for solving non-linear equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1467-1474.
    2. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    3. Deng, Dingwen & Liang, Dong, 2018. "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 188-209.
    4. Belmonte-Beitia, Juan & Pérez-García, Víctor M. & Vekslerchik, Vadym, 2007. "Modulational instability, solitons and periodic waves in a model of quantum degenerate boson–fermion mixtures," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1268-1277.
    5. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    6. Lv, Xiumei & Lai, Shaoyong & Wu, YongHong, 2009. "An auxiliary equation technique and exact solutions for a nonlinear Klein–Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 82-90.
    7. Seadawy, A.R. & El-Kalaawy, O.H. & Aldenari, R.B., 2016. "Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 57-71.
    8. Md. Asaduzzaman & Adem Kilicman & Md. Zulfikar Ali & Siti Hasana Sapar, 2020. "Fixed Point Theorem Based Solvability of 2-Dimensional Dissipative Cubic Nonlinear Klein-Gordon Equation," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    9. Ye, Caier & Zhang, Weiguo, 2015. "Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 49-57.

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