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

Автор(и)

  • S. Bak

DOI:

https://doi.org/10.15407/mag14.01.016

Ключові слова:

дискретне рiвняння синус-Ґордона, нелiнiйнi осциля- тори, двовимiрна ґратка, гетероклiнiчнi рухомi хвилi, критичнi точки, принцип концентрованої компактностi.

Анотація

Статтю присвячено дискретному рiвнянню синус-Ґордона, яке описує нескiнченну систему нелiнiйно зв’язаних нелiнiйних осциляторiв на двовимiрнiй ґратцi iз зовнiшнiм потенцiалом V (r) = K(1 - cos r). Основний результат стосується iснування розв’язкiв у виглядi гетероклiнiчних рухомих хвиль. За допомогою методу критичних точок i принципу концентрованої компактностi отримано достатнi умови iснування таких розв’язкiв.

2010:34G20, 37K60, 58E50.

Посилання

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Опубліковано

2018-06-20

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(1)
Bak, S. The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation With Nonlinear Interaction on a 2D-Lattice. J. Math. Phys. Anal. Geom. 2018, 14, 16-26.

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