The sine-Gordon equation. Kink soliton Soliton: This is a solution of a nonlinear partial differential equation which represent a solitary travelling wave, which:.

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ere nedenfor, nemlig hans hjelpsom het overfor sine tilhengere (sine venner). N either Hellberg nor H ødnebø has presented a convincing solution of this problem. Yet this m etaphor (and the equation of a ship w ith a bear m ust be either a m eta word and a sea or a wave word m ust all be treated as approxim ately  Hence we can replace z by z +z0, where z0 is any constant, in the above solutions of equation (1.4). 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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By Request PDF | Travelling Wave Solutions of Triple Sine–Gordon Equation | Using a complete discrimination system for polynomials and elementary integral method, we obtain the travelling solutions (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 We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We propose a method to deal with the general sine-Gordon equation. 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.

In Section 3, the sine-Gordon expansion method is implemented to produce the exact traveling wave solutions of the Tzitzeica type equations in nonlinear optics; and finally, a short conclusion is provided in Section 4. 2. Description of the sine-Gordon expansion method of the sine-Gordon equation when the underlying wave is a travelling wave.

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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.

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In the present work it is We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We propose a method to deal with the general sine-Gordon equation. 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.
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We have the following theorem: Theorem 1. Kink wave solutions to equation (1) utt = uxx + sin u, are spectrally stable if c2 6= 1. 2.1.

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We propose a method to deal with the general sine-Gordon equation. 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.

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