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Multiple mixed solutions of the nonlocal sine-Gordon equation
European Physical Journal C: Particles and FieldsIn this paper, we propose the nonlocal sine-Gordon equation from the AKNS system by the Parity and the Time symmetries. Moreover, the main work is to construct the Darboux transformation for the nonlocal sine-Gordon equation. In particular, various types
Jian Li +3 more
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Dynamical behavior of water wave phenomena for the 3D fractional WBBM equations using rational sine-Gordon expansion method [PDF]
Scientific ReportsTo examine the dynamical behavior of travelling wave solutions of the water wave phenomenon for the family of 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations, this work employs the rational Sine-Gordon expansion (RSGE) approach based on the ...
Abdulla-Al- Mamun +3 more
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Wobbling Fractals for The Double Sine–Gordon Equation
Symmetry, 2023 This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution. In the case λ = 0, we get the well-known perturbation theory for the sine–Gordon equation.
Attilio Maccari
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A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography
Algorithms, 2021 Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms.
La Zakaria +2 more
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Control for the sine-gordon equation [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2004 The damped sine-Gordon equation with non-homogeneous Dirichlet boundary conditions is considered. Optimal and robust boundary control problems associated to this equation are studied. After a short overview of some classical results concerning the existence and uniqueness of the solution of the sine-Gordon equation, the existence of a solution for the ...
Petcu, Madalina, Temam, Roger
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A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions
Nuclear Physics B, 2020 In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and traveling wave solutions of the (2+1 ...
Gangwei Wang +4 more
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Multiple-scale analysis of the parametric-driven sine-Gordon equation with phase shifts
Open Physics, 2022 In this article, we model the current and voltage across the weak link between two superconductors. This gives us a nonhomogeneous, nonlinear parametric-driven sine-Gordon equation with phase shifts.
Munir Taj +7 more
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Finite size effects and the supersymmetric sine-Gordon models [PDF]
, 2003 We propose nonlinear integral equations to describe the groundstate energy of the fractional supersymmetric sine-Gordon models. The equations encompass the N = 1 supersymmetric sine-Gordon model as well as the phi(id,id,adj) perturbation of the SU(2)(L ...
Dunning, Clare
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The Sine-Gordon solitons in nematic liquid crystals under the external electric field
Results in Physics, 2018 In this paper, we study the dynamic equation of molecular motion in nematic liquid crystals when there exists the twisting disturbance of the molecular arrangement under the external electric field.
Yan Li, Xiaobo Lu, Chunfeng Hou
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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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