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Comments on the perturbed sine–Gordon equation [PDF]
Journal of Mathematical Physics, 1985 We examine the sine–Gordon equation with a perturbation λΔV. We derive necessary conditions on ΔV such that the perturbed equation has solutions with finite energy, analytic in λ, and which reduce to the static soliton when the perturbation is removed (λ→0). Several examples illustrating these conditions are presented.
Papastamatiou, N. J. +2 more
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Bäcklund transformations for multidimensional sine-Gordon equations [PDF]
Proceedings of the National Academy of Sciences, 1980 A class of Bäcklund transformations for multidimensional sine-Gordon equations is shown to relate solutions of only one- and two-dimensional equations. Also, a proposed superposition principle is shown to be useless.
Benguria, R., Case, K. M.
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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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Quantum Theory of Self-Induced Transparency [PDF]
, 1995 It is known that classical electromagnetic radiation at a frequency in resonance with energy splittings of atoms in a dielectric medium can be described using the classical sine-Gordon equation.
André LeClair +24 more
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Exceptional discretizations of the sine-Gordon equation
Physical Review E, 2008 20 ...
Barashenkov, I. V., van Heerden, T. C.
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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 $ ^4$ model. We focus, in particular, on two of their prototypical solutions, namely the kink-like heteroclinic connections and the time-periodic, exponentially localized in space breather waveforms.
Chirilus-Bruckner, Martina +3 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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Results in Applied MathematicsIn this paper we investigate the fractional modified Korteweg de Vries-sine-Gordon equation and show the inverse scattering transform method can also be used to obtain soliton solutions of fractional modified Korteweg de Vries-sine-Gordon equation. It is
Bazar Babajanov, Fakhriddin Abdikarimov
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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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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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