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1 Jan 2016 Abstract: In the present study, a B-spline collocation method has been applied to obtain a numerical solution of the sine-Gordon equation. Then The Sine-Gordon Equation (SGE), q_{xt}= sin q, is a well-known soliton equation. 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. 1701-1705.

Sine gordon solution

2.1 Sine–Gordon equation (SGE). 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 31 Jan 2007 In this seminar, we will introduce the Sine-Gordon equation, and solve it We introduced solitons as the solutions to a nonlinear (wave) The first expression corresponds to a single-soliton solution. 2◦ .

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I. INTRODUCTION. Sine Gordon Equation is a partial differential equation which appears in differential As an application, we construct for the matrix sine-Gordon equation N-soliton solutions analogous to the multisoliton solutions for the KdV equation due to This paper develops a local Kriging meshless solution to the nonlinear 2 + 1- dimensional sine-Gordon equation.

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II The sine-Gordon Equation The sine-Gordon equation has conserved quantity E1=12π∫−∞+∞φxdx which equals integer number. This conservation law is called topological chargeof solution φ(x,t). In this work, a local kernel based numerical scheme is constructed for numerical solution of sine-Gordon equation in circular domain. The global kernel method resulted the dense differentiation matrices and hence difficult to apply for problem with large amount of data points. The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave (RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation.

you can post here or e-mail me directly at - Se hela listan på wiki2.org of the sine-Gordon equation when the underlying wave is a travelling wave.
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solution of sine-Gordon equation u = 2arccos[sech z p ¡c]; c < 0: (2.9) Using the identity tan2 u 4 = 1¡cos u 2 1+cos u 2; (2.10) we may write the solution (2.9) in the form u = 4arctan[exp(z p ¡c)]¡…: (2.11) The solutions (2.11) was also given in [7]. Case(2) c0 = c2 2 4c4: In this case, we have k = ¡2. Using v = a1` and equation (1.7), we obtain the following solutions v = †tan z p Another solution to the sine-Gordon equation is given by making the substitution , where , giving the ordinary differential equation. (14) However, this cannot be solved analytically, since letting gives. (15) which is the third Painlevé transcendent (Tabor 1989, p.

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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 question whether solution of sine–Gordon equation still exhibit soliton like behavior under an external forcing has been challenging as it is extremely difficult to obtain an exact solution The magnetic flux trapped in a long Josephson function (two bulk superconductors seperated by a narrow layer of a dielectric material) time-independent kink solutions are computed for the phi^4- and the sine-Gordon theory. The time-dependent kink solutions were then found by Lorentz transformation of the time-independent solutions. Interesting quantities such as the kink mass, the charge and the energy density is computed in both phi^4- and the sine-Gordon theory. A breather is a localized periodic solution of either continuous media equations or discrete lattice equations.

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Interesting quantities such as the kink mass, the charge and the energy density is computed in both phi^4- and the sine-Gordon theory. A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sine-Gordon equation and the focusing nonlinear Schrödinger equation are examples of one-dimensional partial differential equations that possess breather solutions. This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. solution of sine-Gordon equation u = 2arccos[sech z p ¡c]; c < 0: (2.9) Using the identity tan2 u 4 = 1¡cos u 2 1+cos u 2; (2.10) we may write the solution (2.9) in the form u = 4arctan[exp(z p ¡c)]¡…: (2.11) The solutions (2.11) was also given in [7].