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This article is cited in 6 scientific papers (total in 6 papers)
The existence of heteroclinic travelling waves in the discrete sine-Gordon equation with nonlinear interaction on a $\mathrm{2D}$-lattice
S. Bak Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, 32 Ostrozkogo St., Vinnytsia, 21001, Ukraine
Abstract:
The article deals with the discrete sine-Gordon equation that describes an infinite system of nonlinearly coupled nonlinear oscillators on a $\mathrm{2D}$-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.
Key words and phrases:
discrete sine-Gordon equation, nonlinear oscillators, 2D-lattice, heteroclinic travelling waves, critical points, concentration-compactness principle.
Received: 22.06.2017
Citation:
S. Bak, “The existence of heteroclinic travelling waves in the discrete sine-Gordon equation with nonlinear interaction on a $\mathrm{2D}$-lattice”, Zh. Mat. Fiz. Anal. Geom., 14:1 (2018), 16–26
Linking options:
https://www.mathnet.ru/eng/jmag686 https://www.mathnet.ru/eng/jmag/v14/i1/p16
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Abstract page: | 125 | Full-text PDF : | 41 | References: | 20 |
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