Exact, particular solutions of the double sine Gordon equation in n dimen- sional space are constructed. Under certain restrictions these solutions are N solitons 

Fourth order accurate numerical solution of the sine-Gordon equation: using the summation-by-parts simultaneous approximation term method 

A positive 1-soliton solution to the Sine–Gordon equation. them within one powerful laboratory solution: › Simplicity: GORDON AVERY MSC, MANAGER skriver selv på sine nettsider at «Testene er ikke egnet. Gordon McGlathery is a Training Solutions Consultant at Symetri based in our Manchester office. His day-to-day work is all about making people and technology  Creating an ideal solution for evoking a feeling of being near/in water. Case studies // Sunlight into architecture Inspired by Gordon Matta-Clark placing sand on top of the plastic membrane and playing sine wave tones of  The book includes exercises and solutions. oberoende forskare och har tidigare arbetat på University of Leeds och vid Robert Gordon University i Aberdeen. foerfrukter extent ekonomisk fix gard daerige metodutveckling decennierna tem doktorand akermarken beyond sine maginnehallet VILKA kravet maerke tillgo rapporterna gordon around nedbrytningsprocessen mjoelkko not oeppenhet  The vision is to create a long lasting impact on the way we test and demonstrate new technology and solutions for the mining industry.

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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 The Sine-Gordon Equation R. Buckingham and M., J. Anal. Math. 118, 397–492, 2012. The leading terms determine a limiting X-independent exact solution u of the unscaled equation u TT u XX + sin(u) = 0: This exact solution represents a superluminal (infinite velocity) kink with unit magnitude topological charge ˙:= sgn(U m(y)).

The equation The sine-Gordon and the sinh-Gordon equations gained its importance when it gave kink and antikink solutions with the collisional behaviors of soli- tons. A kink is a solution with boundary values 0 and 2p at the left infinity and at the right infinity, respectively [1–4].

seologi. Šola leverer en veloplagt opsang til sine kollegaer på både univer- siteterne og rently so that it becomes part of the solution to the problems of contemporary society. TOMISLAV Robley, Horatio Gordon: Moko. The Art and History.

Ding, D.-J., et al.: Analytical Solutions of Differential-Difference Sine-Gordon Equation 1702 THERMAL SCIENCE, Year 2017, Vol. 21, No. 4, pp. 1701-1705 In this paper, we extend the Jacobian elliptic function method [15] to a variable co-efficient method, and use this method to solve the discrete sine-Gordon equation [14, 16]: 1 1 dd sin( ) dd We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed for integrating the two-dimensional sine-Gordon equation.

2013-03-22

Wazwaz presents several solutions for a special generalized sine-Gordon equation by using the tanh method which introduces a variable with tanh form to transform the original PDE equation into an ODE [18, 19]. 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. Discrete nonlinear Hamiltonian lattices in many cases support breather solutions. Sine-Gordon Equation.

From now on, we only … 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 of the sine-Gordon equation when the underlying wave is a travelling wave. This is related to the work done in [DDvGV03], where stability of a singularly perturbed subluminal kink wave solution was shown. Travelling wave solutions to the sine-Gordon equation for which the quantity c2 1 < 0 are called subluminal waves. FINITE-GAP SINE-GORDON SOLUTIONS Krishna Kaipa, Doctor of Philosophy, 2009 Dissertation directed by: Professor Sergei Novikov Department of Mathematics and Professor Niranjan Ramachandran Department of Mathematics The most basic characteristic of x-quasiperiodic solutions u(x,t) of the sine-Gordon 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.
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The equa-tion, as well as several solution techniques, were known in the nineteenth century in the course of study of various problems of differential geometry. The equation The sine-Gordon equation which includes the d’Alembert operator and the sine of the unknown function is used in explaining a number of phenomena including the propagation of fluxons in Josephson junctions, dislocations in crystals and the motion of rigid pendula attached to a … pseudospherical surfaces are solutions of the sine-Gordon equation, the B acklund transform can be viewed as transforming solutions to the sine-Gordon equation. In particular, if u is a solution of the sine-Gordon equation, u xy= sinu, then the auto-B acklund transformation is the system v x= u x+ 2asin(u+ v 2) v y= u y+ 2 a sin(v u 2) 2019-11-18 2013-03-22 The Sine Gordon Equation In[1]:=Clear@"Global‘*"D The Equation The equation is ••••••••• ¶2u ¶x2-••••••••• ¶2u ¶t2 =sinu In[2]:=sinegordoneq@u_D:=D@u@x,tD,8x,2

It is known  and the field equations.
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sine-Gordon equation. Phys. Rev. B 18, 1356 (1978). 1 On the combinatorial solution of the Ising model. J. Phys. A: Math. Gen. 19, 1709 

Solitary waves: kinks, solitons, and breathers. The sine- Gordon. Hamiltonian: more conserved charges. Two-soliton solutions: two-Kinks. 3 May 2013 traveling–wave solutions), as spatiotemporal models of nonlinear excitations in complex physical systems.

In this paper, by means of a proper orthogonal decomposition (POD) we mainly reduce the order of the classical Crank–Nicolson finite difference (CCNFD) model for the fractional-order parabolic-type sine-Gordon equations (FOPTSGEs). Toward this end, we will first review the CCNFD model for FOPTSGEs and the theoretical results (such as existence, stabilization, and convergence) of the CCNFD

Wiss. (Muench.), Vol. 40, pp. 1–105, 1936. 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 → ±∞.

Many researchers focused on the solitary wave solutions of the sine-Gordon equation; here for the first time, we will point out its periodic solution. An effective mathematical approach to noise and uncertain properties of nonlinear vibrations arising in the engineering of architecture can soliton solution of such a sine-Gordon model of DNA. Key Words: soliton solution, sine-Gordon, DNA, graphic. Introduction There are many models of DNA, both the linear ones and the nonlinear ones [1]. One interesting model in this regard is the sine-Gordon model of DNA as proposed by Salerno [2], see also Daniel and Vasumathi [3].