# SINE-GORDON - Uppsatser.se

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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. 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◦ .

1–105, 1936.

## Cornelia Schiebold

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. ### A summary on Solitons in Quantum field 935529/FULLTEXT01.pdfآ

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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17. 182,5. 169,8. 145. STD 62,0 Sine Juul Praastrup. FRI. 36 460 1426,1 Alan Gordon. 94.
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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 . 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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