Periodic traveling waves in Fermi–Pasta–Ulam type systems with nonlocal interaction on 2d-lattice

S. M. Bak; G. M. Kovtonyuk

doi:10.30970/ms.60.2.180-190

S. M. Bak Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University Vinnytsia, Ukraine
G. M. Kovtonyuk Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University Vinnytsia, Ukraine

DOI: https://doi.org/10.30970/ms.60.2.180-190

Анотація

The paper deals with the Fermi--Pasta--Ulam type systems that describe an infinite systems of nonlinearly coupled particles with nonlocal interaction on a two dimensional lattice. It is assumed that each particle interacts nonlinearly with several neighbors horizontally and vertically on both sides. The main result concerns the existence of traveling waves solutions with periodic relative displacement profiles. We obtain sufficient conditions for the existence of such solutions with the aid of critical point method and a suitable version of the Mountain Pass Theorem for functionals satisfying the Cerami condition instead of the Palais--Smale condition. We prove that under natural assumptions there exist monotone traveling waves.

Біографії авторів

S. M. Bak, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University Vinnytsia, Ukraine

Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University
Vinnytsia, Ukraine

G. M. Kovtonyuk, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University Vinnytsia, Ukraine

Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University
Vinnytsia, Ukraine

Посилання

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