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Travelling Wave Solutions of Triple Sine–Gordon Equation @article{Chengshi2004TravellingWS, title={Travelling Wave Solutions of Triple Sine–Gordon Equation}, author={Liu Cheng-shi}, journal={Chinese Physics Letters}, year={2004}, volume={21}, pages={2369-2371} } Se hela listan på scholarpedia.org 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 ) . 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. Double Sine–Gordon equation JacobiAmplitude Traveling wave solution Implicit solution abstract Under the assumption that u0 is a function form of einu, 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 ¼ ku xx þ2asinðnuÞþbsinð2nuÞ 2015-05-28 · Although the Sine-Gordon equation was derived for quite a few physical systems that have nothing to do with Special Relativity, the equation itself emerges as a non-linear relativistic wave equation. This is why in later years it has found applications in theoretical High-Energy Physics (e.g., in Relativistic Quantum Field Theory, and, in recent years, in String Theory).

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 Using a complete discrimination system for polynomials and elementary integral method, we obtain the travelling solutions for triple sine-Gordon equation. This method can be applied to similar problems and has general meaning.

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Rev. av T Ohlsson · Citerat av 1 — "i is the wave function of the baryon B and N is the number operator. N Nu" ^u. " + Nu#^ The solutions (5.8) and (5.9) are eigenstates of the helicity operator. h ^p S; The Klein{Gordon equation does not reveal the full spin.

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check- circle. Text Solution. Solution : Let us compare the given equation Feb 8, 2010 We have already seen such a wave as a solution of the constant coefficient transport equation ut + cux = 0, it can, however, appear in many other String Wave Solutions · Traveling Wave Solution for String · String Traveling Wave Velocity · Traveling Wave Parameters · Plane Wave Expressions. 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). rapidly to accurate solutions.
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Travelling wave solutions of the sine-Gordon equation are written in the form u(x, t) = f(x − ct), where c is the wave speed and f (x): R → R is the wave profile satisfying the following differential equation: 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.

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).
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When c2 − 1 > 0 they are called superluminal waves. We have the following theorem: Theorem 1.

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