Periodic traveling waves in the system of linearly coupled nonlinear oscillators on 2D-lattice

Sergiy Bak

Address: Vinnytsia Mykhailo Kosiubynskyi State Pedagogical University, Faculty of Mathematics, Physics and Computer Science, Ostrozkogo 32, 21001 Vinnytsia, Ukraine

E-mail: sergiy.bak@gmail.com

Abstract: In this paper we obtain results on existence of non-constant periodic traveling waves with arbitrary speed $c>0$ in infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. Sufficient conditions for the existence of such solutions are obtained with the aid of critical point method and linking theorem.

AMSclassification: primary 34C15; secondary 37K58, 37K60, 74J30.

Keywords: nonlinear oscillators, 2D-lattice, traveling waves, critical points, linking theorem.

DOI: 10.5817/AM2022-1-1