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On solitary wave solutions of a class of nonlinear partial differential equations based on the function 1/coshn(αx+βt)

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  • Vitanov, Nikolay K.
  • Dimitrova, Zlatinka I.
  • Ivanova, Tsvetelina I.

Abstract

The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used simplest equation is fξ2=n2(f2−f(2n+2)/n). The developed methodology is illustrated on examples of classes of nonlinear partial differential equations that contain: (i) only monomials of odd grade with respect to participating derivatives; (ii) only monomials of even grade with respect to participating derivatives; (iii) monomials of odd and monomials of even grades with respect to participating derivatives. The obtained solitary wave solution for the case (i) contains as particular cases the solitary wave solutions of Korteweg–deVries equation and of a version of the modified Korteweg–deVries equation. One of the obtained solitary wave solutions for the case (ii) is a solitary wave solution of the classic version of the Boussinesq-type equation.

Suggested Citation

  • Vitanov, Nikolay K. & Dimitrova, Zlatinka I. & Ivanova, Tsvetelina I., 2017. "On solitary wave solutions of a class of nonlinear partial differential equations based on the function 1/coshn(αx+βt)," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 372-380.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:372-380
    DOI: 10.1016/j.amc.2017.07.064
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    References listed on IDEAS

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    1. 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.
    2. Vitanov, Nikolay K. & Dimitrova, Zlatinka I. & Vitanov, Kaloyan N., 2015. "Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 363-378.
    3. Kudryashov, Nikolai A. & Demina, Maria V., 2007. "Polygons of differential equations for finding exact solutions," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1480-1496.
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