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arXiv · 1708.01901

Solitary wave solutions of nonlinear partial differential equations based on the simplest equation for the function $1/\cosh^n$

Nikolay K. Vitanov·Zlatinka I. Dimitrova·Tsvetelina I. Ivanova
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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 $f_\xi^2 = n^2(f^2 -f^{(2n+2)/n})$. The developed methodology is illustrated on two 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. 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.

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Nikolay K. Vitanov, Zlatinka I. Dimitrova, Tsvetelina I. Ivanova. 2017-08-06. Solitary wave solutions of nonlinear partial differential equations based on the simplest equation for the function $1/\cosh^n$. https://arxiv.org/abs/1708.01901

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