Jan 31, 2007 In this seminar, we will introduce the Sine-Gordon equation, and solve it Figure 2: This image shows an imperfect moving breather. 19

Thermodynamics of the Boltzmann gas consisting of solitons, antisolitons, and breathers of the classical sine-Gordon system is studied by taking their interactions into account. A compact expression for the thermodynamic potential is obtained, which agrees with that obtained from the classical limit of the Bethe-ansatz formulation of the quantum sine-Gordon thermodynamics.

We have also carried out L'equazione di sine-Gordon (o equazione di seno-Gordon) è un'equazione differenziale alle derivate parziali iperbolica non lineare in 1 + 1 dimensioni, che coinvolge l'operatore di d'Alembert e il seno della funzione incognita. È stata originariamente introdotta da Edmond Bour (nel 1862) nel corso dello studio delle superfici a curvatura negativa costante, come l'equazione di Gauss Ejemplos del primer caso son la ecuación de sine-Gordon [1] y la ecuación no lineal de Schrödinger. [2] Una condición necesaria para la existencia en el segundo caso (redes discretas no lineales), es que la frecuencia principal del breather y sus armónicos se encuentren fuera del espectro de frecuencias de los fonones de la red, esto es, las frecuencias del breather y de la red deben ser Thermodynamics of the Boltzmann gas consisting of solitons, antisolitons, and breathers of the classical sine-Gordon system is studied by taking their interactions into account. A compact expression for the thermodynamic potential is obtained, which agrees with that obtained from the classical limit of the Bethe-ansatz formulation of the quantum sine-Gordon thermodynamics. This content has been downloaded from IOPscience.

Sine gordon breather

Sine-Gordon standing breather is a swinging in time coupled kink-antikink 2-soliton solution. Large amplitude moving sine-Gordon breather. A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1 + 1) dimensions. The main motivation of our study is to test the ideas Our main ﬁnding is that the breather of the sine-Gordon model will only persist at the interface between gain and loss that-symmetry imposes but will not be preserved if centered at the lossy or at the gain side.

Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Sine-Gordon Breather Dynamics To cite this article: Alwyn C Scott 1979 Phys.

breather (i.e., not a standing wave) and the conditions under which it can persist in a -symmetric medium. As our model of interest, we will explore the sine-Gordon equation in the presence of a -symmetric perturbation. Our main ﬁnding is that the breather of the sine-Gordon model will only persist at

D plasma waves. D a soliton! D chain of solitons. D resistive state.

The Breather Surface: The Breather surface is the surface of Gaussian curvature minus one that corresponds to the following solution of the Sine-Gordon

Scattering of two sine-Gordon breathers. Scattering of Kortweg-Devries solitons on a periodic grid. Lecture Notes. Low-intensity light pulses in optical fibers propagate linearly but dispersively (as described in “Solitons in the Sine-Gordon Equation”). This dispersion tends to 7 Feb 2018 loops show the performance of the scheme for kinks and breathers initial tial differential equations; graph theory; sine–Gordon equation.

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sine-Gordon Gleichung: Solitonen und Breather Christoph Dreißigacker Im Proseminar Theoretische Physik 02.

Scattering of a SG breather by localized defects has been investigated in the conservative case [53].
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breather of the sine-Gordon model will only persist at the interface between gain and loss that PT -symmetry. imposes but will not be preserved if centered at the lossy or at the gain side.

We analyse the scattering of sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well.

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In this note we prove that the sine-Gordon breather is the only quasimonochromatic breather in the context of nonlinear wave equations in $$\mathbb {R}^N$$ .

Explicit results and plots are presented for 2021-03-22 · This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity.

We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1 + 1) dimensions. The main motivation of our study is to test the ideas

A full two-dimensional simulation showing that azimuthal perturbations remain small allows us to reduce the problem to the one-dimensional radial sine-Gordon equation. We solve this equation on an interval [r 0,r 1] and absorb all outgoing radiation. As the kink shrinks OSTI.GOV Journal Article: Interaction between sine-Gordon breathers. Interaction between sine-Gordon breathers.

Phys. B 705, 447 (2005)], there exists a noncommutative deformation of the sine-Gordon model which remains (classically) integrable but features a second scalar field.