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Geometry and the Sine-Gordon equation

, 1994
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Rogue periodic waves of the sine–Gordon equation

Applied Mathematics Letters, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruomeng Li, Xianguo Geng
exaly   +3 more sources

DISCRETE SINE-GORDON EQUATION

Nonlinear Physics, 2003
M.Ablowitz, M. Boiti, F. Pempinelli, B.
BOITI, Marco, PEMPINELLI, Flora, PRINARI, Barbara, A. SPIRE   +3 more
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The geometry of the sine-gordon equation

Journal of Mathematical Sciences, 1994
See the review in Zbl 0741.35072.
Poznyak, Eh. G., Popov, A. G.
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Breather Dynamics of the Sine-Gordon Equation

Communications in Theoretical Physics, 2013
Summary: 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.
Johnson, Stephen, Biswas, Anjan
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A simple treatment of the sine-Gordon equation

Journal of Mathematical Physics, 2001
To avoid difficulties due to the complexity of the Lax pair of the sine-Gordon equation, the orthogonality relations of the squared Jost solutions is derived simply using the 1+1 dimensional Green’s theorem. The direct perturbation theory for sine-Gordon in the laboratory reference is re-developed, correcting some numerical coefficients in published ...
Chen, Shi-Rong, Huang, Nian-Ning
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The exploding solitons of the sine–Gordon equation

Applied Mathematics Letters
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Shuzhi Liu, Deqin Qiu
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Localization of the sine-Gordon equation solutions

Communications in Nonlinear Science and Numerical Simulation, 2016
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A. V. Porubov, Alexander L. Fradkov, R. S. Bondarenkov, Boris R. Andrievsky   +3 more
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Statistical Mechanics of the Sine-Gordon Equation

Physical Review Letters, 1986
We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta.
, Timonen, , Stirland, , Pilling, , Cheng, , Bullough   +4 more
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Bäcklund transformations for the sine–Gordon equations

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1976
Abstract The generalized sine–Gordon equations z,xt = F(z) in two independent variables x, t include the sine–Gordon z,xt = sin z and the multiple sine–Gordon’s like z,xt = sin z + ½ sin ½z. Among other physical applications all these sine–Gordon’s are significant to the theory of intense ultra-short optical pulse propagation.
Dodd, R. K., Bullough, R. K.
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