Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 1, pp. 16-26   https://doi.org/10.15407/mag14.01.016     ( to contents , go back )
https://doi.org/10.15407/mag14.01.016

The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice

S. Bak

Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, 32 Ostrozkogo St., Vinnytsia, 21001, Ukraine
E-mail: sergiy.bak@gmail.com

Received June 22, 2017.

Abstract

The article deals with the discrete sine-Gordon equation that describes an infinite system of nonlinearly coupled nonlinear oscillators on a 2D-lattice with the external potential V (r) = K(1 - cos r). The main result concerns the existence of heteroclinic travelling waves solutions. Sufficient conditions for the existence of these solutions are obtained by using the critical points method and concentration-compactness principle.

Mathematics Subject Classification 2000: 34G20, 37K60, 58E50.
Key words: discrete sine-Gordon equation, nonlinear oscillators, 2D-lattice, heteroclinic travelling waves, critical points, concentration-compactness principle.

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