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Breather Dynamics of the Sine-Gordon Equation
Communications in Theoretical Physics, 2013Summary: 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, 2001To 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 LetterszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shuzhi Liu, Deqin Qiu
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Localization of the sine-Gordon equation solutions
Communications in Nonlinear Science and Numerical Simulation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. V. Porubov +3 more
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Statistical Mechanics of the Sine-Gordon Equation
Physical Review Letters, 1986We 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 +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, 1976Abstract 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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Journal of Mathematical Physics, 1970
The equation φtt − φxx + m2 sin φ = 0 is presented as a model field theory and studied in detail. It exhibits discrete conserved quantities and extended particle states, with the proper behavior regarding covariance, stability, etc. Those particles do not interact with small oscillations, and we show that this (plus a few reasonable requirements ...
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The equation φtt − φxx + m2 sin φ = 0 is presented as a model field theory and studied in detail. It exhibits discrete conserved quantities and extended particle states, with the proper behavior regarding covariance, stability, etc. Those particles do not interact with small oscillations, and we show that this (plus a few reasonable requirements ...
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Physics Letters A, 1989
Abstract Some special types of solutions in the high dimensional sine-Gordon equation can be deformed to that of the double sine-Gordon equation by solving an ordinary differential equation or using a pure algebraic deformation relation.
Sen-yue Lou, Guang-jiong Ni
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Abstract Some special types of solutions in the high dimensional sine-Gordon equation can be deformed to that of the double sine-Gordon equation by solving an ordinary differential equation or using a pure algebraic deformation relation.
Sen-yue Lou, Guang-jiong Ni
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2000
Abstract In this chapter we consider the SG equation under periodic and even periodic boundary conditions (see Example 2.3 in Section 2.1). The results are parallel to the KdV case and our presentation is much shorter. Missing details can be found in McKean (1981), Belokolos et al.
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Abstract In this chapter we consider the SG equation under periodic and even periodic boundary conditions (see Example 2.3 in Section 2.1). The results are parallel to the KdV case and our presentation is much shorter. Missing details can be found in McKean (1981), Belokolos et al.
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On Euclidean sine-Gordon equations
Physica Scripta, 2012The sine-Gordon equations are considered in Euclidean spaces with dimensionality d = 2 and 4. General N-soliton solutions are constructed for d = 2 by the method of vertex operators. Special solutions with one and two solitons are obtained for d = 4 explicitly.
Jun Sakaguchi, Kiyoshi Sogo
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