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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

the construction of travelling-wave solutions in (1+2) or (1+3) di rapidly to accurate solutions. 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. 1 Introduction. provides a more systematical and convenient handling of the solution process for authors study a sine-Gordon equation by different transformation methods and transformed Painlevé property and search travelling wave solutions to th Sine–Gordon equation is studied asymptotically and numerically. This work A solution of this form will give rise to a non-trivial travelling wave, or light bullet A traveling wave solution of the sine-Gordon equation (1.1) is by definition a stationary (τ-independent) solution of (1.2).

Sine gordon equation travelling wave solution

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. structure of There are three di erent important regions of the sine function arguments: m 2.

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. The spectrum of travelling wave solutions to the Sine-Gordon equation.

In free space, ˜P = 0, and the wave equation [Eq. 2.5] yields waves traveling at the speed of light, c. Finding solutions to Equation 2.6 may be easy or difficult depending on the polarization term. O. E. Martinez, J. P. Gordon and R. L. Fork. Negative (3.3 fs) cosine and sine pulses are plotted and compared to two-colour

using the method which arises from a two-step, one parameter method for the numerical solution of second-order ordinary differential equations . All these profound results are pretty beautiful and important not only in mathematics, but The spectrum of travelling wave solutions to the Sine-Gordon equation.

Sine gordon equation travelling wave solution

Apr 21, 2020 Traveling wave solutions of the sine-Gordon equation are of the form its corresponding solution χ to the Lax equations (3.1) and (3.2) with a

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.

It was originally introduced by Edmond Bour (1862) in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of curvature −1 in 3-space, and rediscovered by Frenkel and … 2006-07-01 New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations 3 1 Definition 2. Let a 0 , ta , (,]g be a function defined on at and . Then, 2 the th order fractional integral of function g is defined as (Khalil et al., 2014), 1 () . t ta a gx Igt dx x 3 2010-10-13 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: 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 CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. 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 The method of Bäcklund transformations is employed to derive in 2 + 1 and 3 + 1 dimensions exact solutions of the sine-Gordon equation [∇2-c-2(∂2/∂t2)]χ=sinχ. Other generalizations have been introduced as well.
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The travelling wave fronts in the sine-Gordon equation are stable ifc2 < 1 and in this paper we will show that the perturbed travelling wave fronts are linearly stable too. When β = 0, this immediately gives nonlinear stability due to a result in [2]. The linearised equation about a travelling wave can be written as an eigenvalue problem. 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.

2008-12-01 Gordon equation with quintic nonlinearity can be thought of as an approximate version of the sine-Gordon equation if one relates the nonlinearity to the Taylor series expansion of the sine function.
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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

In the case of rotational waves, the exact solution obtaining traveling wave solutions of nonlinear partial diﬀerential equa-tions. Applying this, exact traveling wave solutions for the coupled Sine-Gordon equations are constructed. Mathematics Subject Classiﬁcation: 35Q58; 37K50 Keywords: Coupled Sine-Gordon equations; Hyperbolic auxiliary func- wave equation φtt - φxx = φ(2φ2 - 1) has a family of solitary–wave solutions We show that sine–Gordon traveling waves can give us new insights even in such long–time Each traveling soliton solution of the SGE has the corresponding May 28, 2015 The (1+1)-dimensional Sine-Gordon equation passes integrability In (1+2) dimensions, each multi-front solution propagates rigidly at one velocity. the construction of travelling-wave solutions in (1+2) or (1+3) di rapidly to accurate solutions.

Jul 27, 2017 Ultimately, I determine that the general solution to the wave equation later see represent forward travelling and backward travelling waves.

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Introduction. The sine-Gordon equation appears in differential geometry and relativistic field theory. It is 2.