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Sine-Gordon Equation: From Discrete to Continuum [PDF]
, 2014 In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine- Gordon equation and the non-integrable φ4 model.
P. G. Kevrekidis +7 more
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On robust stability of sine-Gordon equation [PDF]
2019 IEEE 58th Conference on Decision and Control (CDC), 2019 A perturbed sine-Gordon equation is considered under the restrictions on the model parameters corresponding to the single equilibrium in the noise-free case. First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given.
Efimov, Denis +2 more
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Exceptional discretizations of the sine-Gordon equation
Physical Review E, 2008 Recently, the method of one-dimensional maps was introduced as a means of generating exceptional discretisations of the $ϕ^4$-theories, i.e., discrete $ϕ^4$-models which support kinks centred at a continuous range of positions relative to the lattice. In this paper, we employ this method to obtain exceptional discretisations of the sine-Gordon equation
Barashenkov, I. V., van Heerden, T. C.
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Results in Physics, 2021 Stable soliton solutions for the nonlinear Klein–Gordon equation in condensed matter physics, particle physics, nonlinear optics, solid state physics and the gas dynamics equation ensuing in shock fronts have been established by putting use of the sine ...
Md. Abdul Kayum +4 more
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Results in Physics, 2021 This paper recovers cubic–quartic optical solitons for perturbed Fokas–Lenells equation in polarization-preserving fibers and birefringent fibers. The perturbation terms appear with maximum permissible intensity. Singular and dark solitons, together with
Yakup Yıldırım +6 more
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The solitary wave solutions to the Klein–Gordon–Zakharov equations by extended rational methods
AIP Advances, 2021 In this paper, using the extended rational sine–cosine and rational sinh–cosh methods, we find new soliton solutions for the Klein–Gordon–Zakharov equations.
Shao-Wen Yao +5 more
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Solutions of the Hyperbolic sine–Gordon Equations [PDF]
International Journal of Theoretical Physics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Coupled Sine-Gordon Systems in DNA Dynamics
Advances in Mathematical Physics, 2018 We consider a model called the coupled sine-Gordon equation for DNA dynamics by introducing two double helix structures. The second double helix structure is unilaterally influenced by the first one. The completely integrable coupled sine-Gordon equation
Liya Liu, Chuanzhong Li
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MULTISCALE EXPANSION OF THE LATTICE SINE–GORDON EQUATION [PDF]
Difference Equations, Special Functions and Orthogonal Polynomials, 2007 We expand a discrete--time lattice sine--Gordon equation on multiple lattices and obtain the partial difference equation which governs its far field behaviour. Such reduction allow us to obtain a new completely discrete nonlinear Schröedinger (NLS) type equation.
JI X. D, LEVI, Decio, PETRERA M.
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Salient features of dressed elliptic string solutions on $$\mathbb {R}\times \hbox {S}^2$$ R×S2
European Physical Journal C: Particles and Fields, 2019 We study several physical aspects of the dressed elliptic strings propagating on $$\mathbb {R} \times \mathrm {S}^2$$ R×S2 and of their counterparts in the Pohlmeyer reduced theory, i.e. the sine-Gordon equation.
Dimitrios Katsinis +2 more
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