av E Olofsson · 2017 — Abstract: Solitons are solutions to classical field equations that are of solitons, like sine-Gordon kinks, vortices and magnetic monopoles, that
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The solution of the sine-Gordon equation (Example 1), Equation 8, when p!1, will be as follows: = 0 + 1 + 2; (18) which is in good agreement with that obtained by ADM [37]. The behavior of u(x;t) obtained by HPM, with di erent values of time, is shown in Figure 1. 5. Matrix sine-Gordon equation and its kink solutions. It is well known in the commutative case that one may obtain reductions by imposing periodic conditions on the θ n. Similarly in the non-Abelian case, one can make periodic reductions of . From now on, we only … of the sine-Gordon equation when the underlying wave is a travelling wave.
Sine-Gordon Equation In this talk, by applyingthe IST and the Marchenko method, we get explicit solutions to the sine Gordon equation. Representing the kernels of the Marchenko equation in a separated form by using 2020-04-14 · The fractional sine-Gordon equation with the Riemann–Liouville fractional derivative is used as an example to solve its periodic solution by the homotopy perturbation method. The frequency–amplitude relationship is obtained, and the effect of the fractional derivative order on the vibration property is discussed. Notes on The Sine Gordon Equation David Gablinger January 31, 2007 Abstract In this seminar, we will introduce the Sine-Gordon equation, and solve it using a Baecklund transfomation. Furthermore, we also give a numeric solution using a split-step algorithm, and also present two physical applications of the Sine-Gordon equation.
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Matrix sine-Gordon equation and its kink solutions. It is well known in the commutative case that one may obtain reductions by imposing periodic conditions on the θ n. Similarly in the non-Abelian case, one can make periodic reductions of . From now on, we only … Klein–Gordon equation4,5 in some special cases.
26 Dec 2017 The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized
Below the wave for the SEG soliton solution q is shown as the graph of the 31 Jan 2006 the sine-Gordon equation for the phase difference in a finite spatial interval: solutions of this kind were not considered in previous literature. 4 Sep 2016 Analytical Solutions of Differential-Difference Sine-Gordon Equation. THERMAL SCIENCE, Year 2017, Vol. 21, No. 4, pp.
Several topics involving renormalization group ideas are reviewed. The solution of the s-wave Kondo
In both cases (1) and (2), the sine-Gordon equation admits a Lax representation $$ \frac{\partial L }{\partial t } = [ L, M] , $$ where $ L $ and $ M $ are linear operators and $ [ L, M] = LM - ML $. This enables one to obtain solutions of the Cauchy problem by using the inverse scattering method. 2018-12-01 · As an integrable PDE, the sine-Gordon (sG) equation can be solved by means of the inverse scattering transform [, ], and also be transformed to integrable Hamiltonian systems following the r-matrix approach [, ].
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(mathematics) A positive 1-soliton solution to the Sine–Gordon equation. Exempel. We couldn't Gordon Security Solutions.
Travelling wave solutions to the sine-Gordon equation for which the quantity c2 1 < 0 are called subluminal waves. The sine-Gordon Equation on a Finite Interval 519 We are interested in the large time asymptotic behavior of the solution of such prob-lems, and in understanding the generation of solitons and assessing their asymptotic role. It is well known that the solution of the initial value problem on the whole line decom-
OSTI.GOV Journal Article: On the numerical solution of the sine-Gordon equation
Multi-soliton solutions can be obtained through continued application of the Bäcklund transform to the 1-soliton solution, as prescribed by a Bianchi lattice relating the transformed results.
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12 Dec 2012 Title:Numerical Solutions to the Sine-Gordon Equation Abstract: The sine- Gordon equation is a nonlinear partial differential equation. It is known
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 triplet of constant matrices.