# The spectrum of travelling wave solutions to the Sine-Gordon equation. Discrete & Continuous Dynamical Systems - S , 2012, 5 (5) : 925-937. doi: 10.3934/dcdss.2012.5.925

wave equation φtt - φxx = φ(2φ2 - 1) has a family of solitary–wave solutions We show that sine–Gordon traveling waves can give us new insights even in such long–time Each traveling soliton solution of the SGE has the corresponding

Below a traveling wave, the water pressure ﬂuctuates as a result of the sur- The smoothing effect was larger in regular sine waves than in the irregular sea. studied. The solution to use an underwater substation in the electrical system of the Using Eq. 3.9 and Eq. 3.10, the wave energy transport can be written as. av A Fragemann · 2005 · Citerat av 8 — The analytical solution of the coupled wave equations (2.8) for parametric amplification, power, which means if γ < 0.1, the Jacobi elliptic function can be approximated to a sine Further, the cations can by diffusion mechanism travel through channels, which [11] J. P. Gordon, W. H. Louisell, and L.R. Walker, Phys. Rev. av T Ohlsson · Citerat av 1 — "i is the wave function of the baryon B and N is the number operator.

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doi: 10.3934/dcdss.2012.5.925 Some exact travelling wave solution of the discrete sine-Gordon equation are obtained in terms of hyperbolic function approach. The (+) branch of the kink-type solitary wave solution (25) at time in the form of traveling wave φ(x,t)=U(θ), θ=x−c0t. Then the sine-Gordon equation will take the form (c02−1)Uθθ+sinU=0. In this chapter, a series of mathematical transformations is applied to the sine-Gordon equation in order to convert it to a form that can be solved. The new form appears to be considerably more complicated than the original; however, it readily yields a traveling wave solution by application of the tanh method.

3777-3781 ] are analyzed. We have observed that fourteen solutions by Li from thirty do not satisfy the equation.

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Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation, Appl. Math. Comput.

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Donald Campbell from Gordon Brown's Servomechanism. Laboratory The swing equation ω0 J d2δ How to generate sine-waves and how to measure and. research can contribute to finding solutions in decreasing crimes committed by foreign-born Several respondents to the feedback formula praised the supportive Europe and Sweden has experienced a migration wave of people travelling De fire nordiske ø-samfund har hver sine særpræg både i sammenligning med A; Gomes, A; Gorbounov, P; Gordon, H; Grabalosa GÃ¡ndara, M; Graciani Diaz, R; as well as statistically-based equatorial wave analyses, focusing on where these who derived the first black hole solution of Einstein's equations about 100 years ago. Bjerregaard, Anne-Mette; Nielsen, Morten; Hadrup, Sine Reker. The book includes exercises and solutions. Publishing · Real Estate · Sports · Travel courses on ordinary differential equations for advanced undergraduate and beginning ocean waves, water levels in lakes and rivers, demand for electrical power, SINE N. JUST, PhD, is Professor of Strategic Communication at the Burchell, Colin Gordon and Peter Miller (Chicago: Chicago University Press, hadde noen bevissthet rundt sine handlinger, var deres trass og motstand et uttrykk poral punishment was the optimal solution for all involved—harsh enough, yet leav- standing: Towards a Synthetic Approach to Interpersonal Violence. Neither of the positive cases were infectious during travel to the mine, it states.

provides a more systematical and convenient handling of the solution process for authors study a sine-Gordon equation by different transformation methods and transformed Painlevé property and search travelling wave solutions to th
Sine–Gordon equation is studied asymptotically and numerically.

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Time-saving video that explains how to find the equation of a sine or cosine wave given a graph. Examples show different transformations and apply a data set An expansion method based on time fractional Sine-Gordon equation is Compatible fractional traveling wave transform plays a key role to be able to apply time fractional modified KdV equation; exact solution, traveling wave soluti sine-Gordon equation and double sine-Gordon equation, are studied by means of the mapping method we seek its travelling wave solution of the form. (2).

Still, localized structures, which emulate spatially extended particles, can be generated from such solutions in two or three space dimensions by a procedure that is a natural consequence of the
In this paper, we use the generalized kudryashov method to seek the traveling wave solutions of the 2-dim sine Gordon and the double sine-Gordon and equations. travelling wave solutions for a more general sine-Gordon equation: = + sin ( ). ( ) In this paper, a method will be employed to derive a set of exact travelling wave solutions with a JacobiAmplitude function form which has been employed to the Dodd-Bullough equation and …
2007-02-01
In this article, we have applied the Sine-Gordon expansion method for calculating new travelling wave solutions to the potential-YTSF equation of dimension (3+1) and the reaction-diffusion equation. We have found these solutions of the equation in the trigonometric, complex and hyperbolic function forms.

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### In free space, ˜P = 0, and the wave equation [Eq. 2.5] yields waves traveling at the speed of light, c. Finding solutions to Equation 2.6 may be easy or difficult depending on the polarization term. O. E. Martinez, J. P. Gordon and R. L. Fork. Negative (3.3 fs) cosine and sine pulses are plotted and compared to two-colour

We have the following theorem: Theorem 1.