av N KAREINEN — A plane wave arrives from a radio source in direction k and is observed at two stations array, where the antenna aperture D in Equation (3.1) is replaced by the lin- ear size of nals travel through multiple intermediate stages in the VLBI back-end before the sampled the cross-correlated bits with a sine and cosine terms.

Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions

doi: 10.3934/dcdss.2012.5.925 Solutions Traveling wave Let us look for solutions of the sine-Gordon equation φ t t − φ x x = sin ⁡ φ. in the form of traveling wave φ (x, t) = U (θ), θ = x − c 0 t. Then the sine-Gordon equation will take the form (c 0 2 − 1) U θ θ + sin ⁡ U = 0. Multyplying the latter equation by U θ and integrating with respect to θ one We investigate the spectrum of the linear operator coming from the sine-Gordon equation linearized about a travelling kink-wave solution. Using various geometric techniques as well as some elementary methods from ODE theory, we find that the point spectrum of such an operator is purely imaginary provided the wave speed c of the travelling wave For the (n + 1)-dimensional sine- and sinh-Gordon equations, by using the approach of dynamical systems to a class of travelling wave solutions, in 21 different regions of a five-parameter space 2.2. The tanh method The tanh method is a powerful solution method for the computation of ex- act traveling wave solutions [16–18]. Various extension forms of the tanh method have been developed.

In [5], an extension to wider classes of evolution equations has been ex- amined. 2020-04-01 Under the assumption that u ' is a function form of e inu , this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine-Gordon equation u tt = ku xx + 2 α sin ( nu ) + β sin ( 2 nu ) . (2000) 345] on modulated travelling wave solutions and the work of Piette and Zakrzewski [Nonlinearity 11 (1998) 1103] on radially symmetric, periodic standing wave solutions of the two-dimensional Sine–Gordon equation. In the present work it is Download Citation | New Exact Travelling Wave Solutions for (2+1) dimensional Sine Gordon and Kadomtsev Petviashvili Equations | In this paper, by using the solutions of an auxiliary ordinary 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.

abL=E. av N KAREINEN — A plane wave arrives from a radio source in direction k and is observed at two stations array, where the antenna aperture D in Equation (3.1) is replaced by the lin- ear size of nals travel through multiple intermediate stages in the VLBI back-end before the sampled the cross-correlated bits with a sine and cosine terms.

Two-dimensional sine-Gordon: Let us demonstrate the application of Kudryashov method for ﬁnding the exact travelling wave solutions of the two-dimensional sine-Gordon equation u tt −u xx −u yy +m 2 sinu = 0, (8) and Dodd–Bullough–Mikhailov equation u xt + peu +qe−2u = 0. (9)

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).

Sine gordon equation travelling wave solution

The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation.It is second-order in space and time and manifestly Lorentz-covariant.It is a quantized version of the relativistic energy–momentum relation.Its solutions include a quantum scalar or pseudoscalar field, a field whose

di Matematica e Applicazioni, Universit a \Federico II", V. Claudio 21, 80125 Napoli 2I.N.F.N., Sezione di Napoli, Complesso MSA, V. Cintia, 80126 Napoli email: gaetano. ore@unina.it Abstract The 2-soliton solutions of the sine-Gordon equation show some of the characteristic features of the solitons. The traveling sine-Gordon kinks and/or antikinks pass through each other as if perfectly permeable, and the only observed effect is a phase shift.

Several new exact travelling wave solutions with the form of JacobiAmplitude function are derived for the general sine-Gordon equation by using some reasonable transformation. Compared with previous solutions, our solutions are more general than some of the previous. 1. Traveling Wave Solutions of the Sine-Gordon and the Coupled Sine-Gordon Equations Using the Homotopy-Perturbation Method A. Sadighi1, D.D. Ganji1; and B. Ganjavi2 Abstract. In this research, the Homotopy-Perturbation Method (HPM) has been used for solving sine-Gordon and coupled sine-Gordon equations, which have a wide range of applications in physics. 2017-11-01 Kink Waves Travelling wave solutions to the sine-Gordon equation for which the quantity c2 − 1 < 0 are called subluminal waves. When c2 − 1 > 0 they are called superluminal waves.
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Keywords: Sine-Gordon equation; Coupled sine- Gordon equation; Homotopy-perturbation method;. Traveling wave solution. Keywords: Coupled Sine-Gordon equations; Hyperbolic auxiliary func- tion; Travelling wave solution; Exact solution; Solitary wave solution.

The Third Wave (2003 film).
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EPISODES EQUAL EQUALITY EQUALLY EQUALS EQUATION EQUATIONS GOODS GOODWILL GORBACHEV GORDON GORGEOUS GOSH GOSPEL SIN SINCE SINCERELY SINE SING SINGAPORE SINGER SINGING SINGLE SOLICITORS SOLID SOLIDARITY SOLITARY SOLO SOLUTION SOLUTIONS

We will apply this method to the sine-Gordon, sinh-Gordon, and double-sine-Gordon equations. In addition to the known solutions of theses equations, some new solutions will also be given. II The sine-Gordon Equation ] also presents some exact travelling wave solutions for a more general sine-Gordon equation: 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 some new travelling wave solutions have been derived [ 22 And [ ]alsopresentssomeexact travelling wave solutions for a more general sine-Gordon equation: = + sin ( ).

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dvs til 1. juli 2012, da de fleste medlemsland i EU måtte CE-merke sine produkter. Steel superstructure for the upper tier An effective solution of trussed rakers was Rowecord (Main Roof) Watson Steel (Olympic Stands) by Gordon Mungall, 12.6 Heat equation, 12.2-3 Wave equation Eugenia Malinnikova, NTNU

Discrete & Continuous Dynamical Systems - S , 2012, 5 (5) : 925-937. doi: 10.3934/dcdss.2012.5.925 Solutions Traveling wave Let us look for solutions of the sine-Gordon equation φ t t − φ x x = sin ⁡ φ. in the form of traveling wave φ (x, t) = U (θ), θ = x − c 0 t. Then the sine-Gordon equation will take the form (c 0 2 − 1) U θ θ + sin ⁡ U = 0. Multyplying the latter equation by U θ and integrating with respect to θ one We investigate the spectrum of the linear operator coming from the sine-Gordon equation linearized about a travelling kink-wave solution.