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Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity

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  • Navickas, Z.
  • Ragulskis, M.
  • Telksnys, T.

Abstract

The inverse balancing method for the determination of the necessary conditions of existence of solitary solutions to mth order differential equations with nth order polynomial nonlinearity is presented in this paper. It is shown that the order of possible solitary solutions does not increase if orders of the differential equation and the polynomial nonlinearity increase. Furthermore, the relationships between the order of the solitary solution and the order of the equation (and the nonlinearity) are given in the explicit form.

Suggested Citation

  • Navickas, Z. & Ragulskis, M. & Telksnys, T., 2016. "Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 333-338.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:333-338
    DOI: 10.1016/j.amc.2016.02.049
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    3. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
    4. Sahoo, S. & Saha Ray, S., 2015. "New approach to find exact solutions of time-fractional Kuramoto–Sivashinsky equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 240-245.
    5. Yuan, Wenjun & Meng, Fanning & Huang, Yong & Wu, Yonghong, 2015. "All traveling wave exact solutions of the variant Boussinesq equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 865-872.
    6. Kudryashov, Nikolay A. & Ryabov, Pavel N., 2014. "Exact solutions of one pattern formation model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1090-1093.
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    Cited by:

    1. Zenonas Navickas & Tadas Telksnys & Inga Timofejeva & Minvydas Ragulskis & Romas Marcinkevicius, 2019. "An Analytical Scheme For The Analysis Of Multi-Hump Solitons," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-17, February.
    2. Telksnys, T. & Navickas, Z. & Marcinkevicius, R. & Ragulskis, M., 2018. "Existence of solitary solutions in systems of PDEs with multiplicative polynomial coupling," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 380-388.

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