Physica D 159 (2001) 101–123 Pulse evolution for a two-dimensional Sine-Gordon equation A.A. Minzonia, Noel F. Smythb,∗, Annette L. Worthyc a FENOMEC, Department of Mathematics and Mechanics, IIMAS, Universidad Aut´onoma de M ´exico,

The Sine Gordon equation is ∂2y/∂x2 = 1/v2 ∂2y/∂t2 + ζ sin(y) where sin(y) acts as both a nonlinear term and a dispersion term. The strength of the nonlinear

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Sine gordon

For help on how to identify the adjacent,. Fysik Och Jon Gordon on Twitter. “Imagine if we all lived this.” Michael Leaming 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. Sine-Gordon Equation A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation. The sine-Gordon equation is the classical wave equation with a nonlinear sine source term. This chapter computes a numerical solution by the method of lines (MOL), including detailed discussion of the Matlab routines and the numerical and graphical output.

F or this, w e will use meth-o ds whic hw e elab orated in application to the theory of preheating after in ation [14,15]. With these Sine Gordon Equation with u(x,0)=sin(3*pi*x) and v(x,0)=1 D. Kaya, A numerical solution of the sine-Gordon equation using the modified decomposition method, Applied Mathematics and Computation, 143(2003): 309-317. [11] D. Kaya, An application of the modified decomposition method for two dimensional sine-Gordon equation, Applied Mathematics and Computation, 159(2004): 1-9.

The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this

of the. Sine-. Gordon field theory.

Specifically, a long Josephson-junction is described by the continuous sine-Gordon equation and a Josephson-junction parallel array by its discrete counterpart. This chapter constitute a revision of the physics of such superconducting systems in the light of the sine-Gordon equation.

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Under certain restrictions these solutions The reputed sine-Gordon equation method was developed based on the wave transformation and it functions only for lower-dimensional NLEEs. There are many higher-dimensional NLEEs concerning real life problems and to interpret them explicitly further soliton solutions are needed. 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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The equation is . 2 u x2. 2 u t2 sin u. In[2]:= sinegordoneq u. : D u x, t , x, 2.

6 (20160527) 46 Theorem 6.8.
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Numerical solution of nonlinear sine-Gordon equation with local RBF-based finite difference collocation method. Y AZARI, G GARMANJANI, H RABIEI. 2013.

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Velocities dressed by e-e The sine-Gordon model has a universality and appears in various ﬁelds of physics [9–12]. The two-dimensional (2D) sine-Gordon model describes the Kosterlitz-Thouless transition of the 2D classical XY model [13,14]. The 2D sine-Gordon model is mapped to the Coulomb gas model with logarithmic interaction [15]. The Kondo sine-Gordon model and the massive Thirring model will be derived by identifying that the perturbation expansion terms respectively the commutators of the two theories are identical if certain relations between the quantities of the theories are identi ed. Simple model: the sine-Gordon equation. The simplest and the most frequently used model which describes the dynamics of the Josephson phase in LJJ is the so-called perturbed sine-Gordon equation.

We study certain deformations of the integrable sine-Gordon model (DSG). It is found analytically and numerically several towers of infinite number of anomalous charges for soliton solutions possessing a special space–time symmetry. Moreover, it is uncovered exact conserved charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e.