Results 21 to 30 of about 1,104 (261)
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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Exact solutions to the sine-Gordon equation [PDF]
Journal of Mathematical Physics, 2010 A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable x and the temporal variable t, and they are exponentially asymptotic to integer multiples of 2π as x → ±∞. The solution formulas are expressed explicitly in terms of a real
T. AKTOSUN +2 more
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The nonlinear and nonlocal integrable sine‐Gordon equation
Mathematical Modelling and Analysis, 2005 A new type of the nonlocal sine‐Gordon equation with the generalized interaction term is suggested. Its limit cases, symmetries and exact analytical solutions are obtained. This type of the nonlocal sine‐Gordon equation is shown to possess one‐, two‐ and
P. Miškinis
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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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Symmetry, Integrability and Geometry: Methods and Applications, 2013 Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation.
Kenichi Kondo
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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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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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New Travelling Wave Solutions for Sine-Gordon Equation
Journal of Applied Mathematics, 2014 We propose a method to deal with the general sine-Gordon equation. Several new exact travelling wave solutions with the form of JacobiAmplitude function are derived for the general sine-Gordon equation by using some reasonable transformation.
Yunchuan Sun
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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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