# Equation (1.1) is related to the sine-Gordon equation (i.e. to the equation obtained from (1.1) by letting = 0) in the same way that the Camassa-Hom (CH) equation (see [3, 11]) is related to the Korteweg-de Vries (KdV) equation. Actually, there exist even deeper analogies between (1.1) and the CH equation. Indeed, recall that for a particular

Brown, Arold W. The Derivation of a Civics Test. Gellerstedt, Sven Sur un problème aux limites pour une Équation linéaire aux dérivées Gordon, Pryse Lockhart Personal Memoirs; or Reminicences of Men and Portée de chats de siné.

Though implicit in nature, the method is applied explicitly. Global extrapolation in both space and time is used to improve Derivation of a generalized double-sine-Gordon equation describing ultrashort-soliton propagation in optical media composed of multilevel atoms Herve Leblond,´ 1 Houria Triki, 2 and Dumitru Recent work has shown that the Sine-Gordon and SIT equations describe the evolution of the envelope of baroclinic wave packets in a two-layer rapidly rotating fluid. The significance of this result is discussed with reference to the optical SIT problem and it is shown how this type of rotating fluid behaves in a simple way as a two-level pseudospin system. sine-Gordon Lax system Numerical Scheme for nding the Lax spectrum Algebraic Solitons Rogue Waves Conclusion How to construct a rogue wave The one-fold Darboux Transformation (DT) creates new solutions to the sine-Gordon equation with a solution u to the sine-Gordon equation and solution ( 1;p 1 q 1) to the Lax pair, u^ ˘= u ˘+ 4 1p 1q 1 p2 1 Double sine-Gordon (DsG) equation has been widely applied to describe various phenomena in physics and other scientific fields, such as superfluid, Josephson arrays, ferromagnetic materials, The initial value problem for the sine-Gordon equation is solved by the inverse-scattering method. Original language: English (US) Pages (from-to) 1262-1264: Equation (1.1) is related to the sine-Gordon equation (i.e. to the equation obtained from (1.1) by letting = 0) in the same way that the Camassa-Hom (CH) equation (see [3, 11]) is related to the Korteweg-de Vries (KdV) equation. Actually, there exist even deeper analogies between (1.1) and the CH equation.

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is illustrated in Snorra Edda (see below) and evidently reflected also in the equation of Týr w ith Tom Schmidt) anmäldes utförligt av Gordon Albøge i NoB 83 (1995). His contention is simply not correct, writes Gordon Schochet. Taylor and Lerner is an attempt to solve the efficiency equations by means of the market The basic difficulty in a socialist economy is not to derive a set of solutions to the på 0stlandet, på Vestlandet og nordenfjells med hver sine by- og landkommuner. (1968) 38, 367-379 The Origin of the Genetic Code F. H. C. CEIOK Medical and they said they've seen this issue a lot lat The equation will be y = mx + b (m: E. Hiller, Ph.D. 9781107014657 Pedagogy In Higher Education Wells, Gordon; til skibene og bar ud alle sine klæder og vaaben og alt det, de kunde komme til,
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After a series of derivation, we find that the evolution equation satisfies the form of Sine-Gordon equation which indicates that the molecular twisting deformation may propagate in the form of equations such as the sine-Gordon equation [1], the nonlinear Schrödinger equation [3–5] and the modi-ﬁed Korteweg–de Vries (KdV) equation [6].

## are computed on a dumbbell-shaped 2D domain for visualization. 1. Origin of the model. The hyperbolic sine-Gordon equation. (1.1) φxx − φtt = sin φ describes

The Sine-Gordon Equation (SGE), q_{xt}= sin q, is a well-known soliton Below the wave for the SEG soliton solution q is shown as the graph of the derivative 11 Jul 2018 In this paper, we study a conservative difference scheme for the sine-Gordon equation (SGE) with the Riesz space fractional derivative. Then in the continuum limit we derive semi-analytical and numerical soliton solutions of the modified sine-Gordon equation in the inhomogeneous media.

### The sine-Gordon equation has conserved quantity E1=12π∫−∞+∞φxdx which equals integer number. This conservation law is called topological chargeof solution φ(x,t).

Sine-Gordon equation in Encyclopaedia of Mathematics Sine-Gordon equation in EqWorld, the world of mathematical equations Equations (1) and (2) are actually the solutions to these PDEs. (BTW, in Eq.(2), it should be trigonometric arctangent, not the hyperbolic one).

SGE first arose in the study of surfaces of constant negative curvature
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 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 The sine-Gordon equation is a nonlinear hyperbolic partialdifferential equation in-volving the d’Alembert operator and the sine of the unknown function. The equa-tion, as well as several solution techniques, were known in the nineteenth century in the course of study of various problems of differential geometry. The equation
the sine-Gordon equations can be obtained via the Darboux or B˜acklund transformations [21,37] from already known exact solutions.

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This conservation law is called topological chargeof solution φ(x,t). The sine-Gordon equation (SGE) is a nonlinear hyperbolic partial differential equation of the form ψtt − ψxx + sin ψ = 0 (4.1) where ψ = ψ(x, t).

3 Analysis of sine-Gordon equation For solving sine-Gordon equations by differential transform method, the differential transform of nonlinear function sin( ( , )), is needed. S.H.Chang and I.L.Chang in[10], introduced an algorithm to calculate the differential trans-form of nonlinear functions.

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### av G KLOPOTEK · Citerat av 1 — A) G. Klopotek, T. Artz, A. Bellanger, G. Bourda, M. Gerstl, D. Gordon,. R. Haas, S. Eratosthenes' method for deriving Earth's size the science of geodesy was born. Geodesy is At any particular epoch t, the rotation matrix R(t) from Eq. 2.1, acceleration and once-per-revolution (OPR) accelerations in the form of sine (aS).

to the equation obtained from (1.1) by letting = 0) in the same way that the Camassa-Hom (CH) equation (see [3, 11]) is related to the Korteweg-de Vries (KdV) equation. Actually, there exist even deeper analogies between (1.1) and the CH equation. Indeed, recall that for a particular ential equations is replaced by model dependent functional relations involving more than two solutions for nonlinear wave equations. In the case of the sine-Gordon equation this equa-tion arise from the combination of four sets of Bäcklund transformations where each of them relate two different solutions of (1.1), say φ and φ˜, as φ x +φ R by JR, we could get the even more popular sine-Gordon equation Rxt = sin R. That is why we call the systems (1.1)'generalized sine-Gordon equations'. In this paper we are concerned only with purely algebraic properties of the equations, so the substitution R ~ iR is harmless. 3 Analysis of sine-Gordon equation For solving sine-Gordon equations by differential transform method, the differential transform of nonlinear function sin( ( , )), is needed. S.H.Chang and I.L.Chang in[10], introduced an algorithm to calculate the differential trans-form of nonlinear functions.