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Kinklike solutions of fourth-order differential equations with a cubic bistable nonlinearity

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Abstract

For the equation y (4)+2y(y 2−1) = 0, we suggest an analytic construction of kinklike solutions (solutions bounded on the entire line and having finitely many zeros) in the form of rapidly convergent series in products of exponential and trigonometric functions. We show that, to within sign and shift, kinklike solutions are uniquely characterized by the tuple of integers n 1, …, n k (the integer parts of distances, divided by π, between the successive zeros of these solutions). The positivity of the spatial entropy indicates the existence of chaotic solutions of this equation.

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Authors and Affiliations

  1. Institute for Mathematics, National Academy of Sciences, Kyiv, Ukraine

    A. M. Samoilenko & I. L. Nizhnik

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  1. A. M. Samoilenko
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  2. I. L. Nizhnik
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Correspondence to A. M. Samoilenko.

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Original Russian Text © A.M. Samoilenko, I.L. Nizhnik, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 2, pp. 201–209.

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Samoilenko, A.M., Nizhnik, I.L. Kinklike solutions of fourth-order differential equations with a cubic bistable nonlinearity. Diff Equat 50, 203–212 (2014). https://doi.org/10.1134/S0012266114020074

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