# Keywords: Bifurcation theory, solitary wave solution, periodic wave solution, (2+1 )-. dimensional sine-Gordon equation. 1. Introduction. In recent years, nonlinear

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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. We have the following theorem: Theorem 1. Kink wave solutions to equation (1) utt = uxx + … 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 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.

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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. 215 (2009). 3777-3781 ] are analyzed. We have observed that fourteen solutions by Li from thirty do not satisfy the equation. The other sixteen exact solutions

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).

### Sine-wave exciting circuit for quartz vibrating gyroscope. geometry: methods and applications ultradiscrete sine-gordon equation over symmetrized max-plus

an insolvent debtor and about the principles and solutions that were stated in ciple of “no punishment without law” (nulla poena sine lege).

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In the paper, we ﬁrst make the travelling wave 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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### 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

, only the ﬁrst solution is meaningful. 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]. Case(2) c0 = c2 2 4c4: We propose a method to deal with the general sine-Gordon equation.

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### Exact Solutions > Nonlinear Partial Differential Equations > Second-Order Hyperbolic Partial Differential Equations > Sine-Gordon Equation 6. @2w @t2 = a @2w @x2 + bsin(‚w). Sine-Gordon equation. It arises in differential geometry and various areas of physics. 1–. Traveling-wave solutions: w(x,t) = 4 ‚ arctan ‰ exp • ± b‚(kx+„t

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