Geodesic
Nonlinear summation of power series and exact solutions of evolution equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 34-41

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The technique of quadratic and cubic summation of power series of the perturbation method was first applied to find exact solutions of nonlinear evolution equations. To build the series they used exponential partial solutions of the linearized equations. Features of the method are demonstrated by solving both the classic and the modified nonintegrable Korteweg-de Vries equations, the modified Burgers equation and the Fisher equation. We obtain exact solitary-wave solutions of the equations in the form of wave pulse and wave front and show that the summation process parameters are determined by the pole orders of the sought-for solutions.
Keywords: summation of power series, nonlinear evolution equations, exact solitary-wave solutions.
Mots-clés : perturbation method 
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     author = {A. I. Zemlyanukhin and A. V. Bochkarev},
     title = {Nonlinear summation of power series and exact solutions of evolution equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {34--41},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_1_a4/}
}
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A. I. Zemlyanukhin; A. V. Bochkarev. Nonlinear summation of power series and exact solutions of evolution equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 34-41. http://geodesic.mathdoc.fr/item/IVM_2018_1_a4/