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Existence of traveling solitary waves in Fermi–Pasta–Ulam-type systems with saturable nonlinearities on 2D-lattice

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Abstract

Systems of the Fermi–Pasta–Ulam type with saturable nonlinearities that describe infinite systems of particles on a two dimensional lattice have been analyzed. The main result concerns the existence of traveling solitary-wave solutions with vanishing relative displacement profiles. In the framework of the critical point theory, sufficient conditions for the existence of such solutions have been obtained.

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Authors and Affiliations

  1. Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, Vinnytsia, Ukraine

    Sergiy M. Bak & Galyna M. Kovtonyuk

Authors
  1. Sergiy M. Bak
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  2. Galyna M. Kovtonyuk
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Correspondence to Sergiy M. Bak.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 4, pp. 450–461, October–December, 2022.

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Bak, S.M., Kovtonyuk, G.M. Existence of traveling solitary waves in Fermi–Pasta–Ulam-type systems with saturable nonlinearities on 2D-lattice. J Math Sci 270, 397–406 (2023). https://doi.org/10.1007/s10958-023-06353-w

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  • DOI: https://doi.org/10.1007/s10958-023-06353-w

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