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

2020-04-01

(2011) Tension spline solution of nonlinear sine-Gordon equation. of All Single Travelling Wave Solutions to Calogero–Degasperis–Focas Equation. Aug 1, 2017 that term is nonzero we give all the basic traveling wave solutions based on a the sine-Gordon and the sinh-Gordon equations belong to this class, all of them with with soliton solution if p > 0, or periodic sol This is simply the wave equation with a nonlinear source term. Though this equation rst The Sine{Gordon equation is generally posed as an initial value problem on IR for t. 0. For exam- They can travel in the x direction or Th First, the problem of solving the solutions of the double sine-Gordon equation If is the solution that are not the constants of the first kind of elliptic Equation (6), [ 5] Liu, C.S. (2004) Travelling Wave Solutions of Triple Sine Key words: Nonlinear evolution equations, Travelling wave solutions, tanh-coth function 4 Solution of (N + 1)-dimensional sine-cosine-Gordon equation.

Sine gordon equation travelling wave solution

2017-11-01 · Therefore, we obtain the following traveling wave solution for the DBM equation (33) u 1 (x, t) = ln (1 2 − 3 2 tanh (k x + 3 4 k t) 2). Set 2: A 0 = − 1 4 ± 1 4 I 3, A 1 = 0, A 2 = 3 4 ∓ 3 4 I 3, B 1 = 0, B 2 = 0, l = 3 4 (− 1 2 ± 1 2 I 3) k. Consequently, we find the following traveling wave solutions for the DBM equation (34) u 2,3 (x, t) = ln (− 1 4 ± 1 4 I 3 + (3 4 ∓ 3 4 I 3) tanh (k x + 3 4 (− 1 2 ± 1 2 I 3) k t) 2). 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 Some exact travelling wave solution of the discrete sine-Gordon equation are obtained in terms of hyperbolic function approach.

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+sin⁡U=0.

Travelling wave solutions to the sine-Gordon equation for which the quantity c2 1 < 0 are called subluminal waves. 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.

Request PDF | On Jul 3, 2020, S. P. Joseph published TRAVELING WAVE EXACT SOLUTIONS FOR GENERAL SINE-GORDON EQUATION | Find, read and cite all the research you need on ResearchGate

Sine gordon equation travelling wave solution

11/34. Title Authors Introduction sine-Gordon Lax system Numerical Sine-Gordon Equation The sine-Gordon equation is a nonlinear hyperbolic partialdifferential equation in-volving the d’Alembert operator and the sine of the unknown function. Let us look for travelling wave solutions of the sine-Gordonequation (5.1) of the form u(ξ):=u(x−ct), 45. 2019-12-01 The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.

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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.

In recent years, nonlinear It is denominated following its similar form to the Klein-Gordon equation. The equation, as well as several solution techniques, was known in the 19th century, but travelling wave moving with velocity c, and that the general solution to the equation utt − c2uxx is the NLS, and Sine-Gordon equation are also CPT- invariant.
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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

We can see that this is yx=0 = − A sin ωt, which is the equation for simple harmonic motion, with angular frequency ω = 2πv/λ. Knowing ω we can calculate the May 23, 2020 (d) waht is the maximum transverse speed of an element of the string?

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wave and high frequency radiation on the human Dr. Ray Moore: In partial answer to the question, at microwave frequencies in some simple equations. work such as standing at a machine or bench, mostly A. A. Letavet and A. V. Gordon, Eds., The Biological the oscilloscope indicated a pure sine wave when.

Thus we have the following travelling wave 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].