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Discrete sine-Gordon equations
Physical Review D, 1978Various discretizations of the sine-Gordon equation are studied. Hirota's discretization scheme is extended and two alternative discretization schemes are constructed. The associated soliton solutions, B\"acklund transformations, conservation laws, and the inverse scattering equations are obtained.
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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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The geometry of the sine-gordon equation
Journal of Mathematical Sciences, 1994See the review in Zbl 0741.35072.
Poznyak, Eh. G., Popov, A. G.
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Bäcklund transformations for the sine–Gordon equations
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1976The generalized sine–Gordon equations z ,xt = F ( z ) in two independent variables x , t include the sine–Gordon z ,xt
Dodd, R. K., Bullough, R. K.
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Revisiting the inhomogeneously driven sine–Gordon equation
Wave Motion, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jagtap, Ameya D. +3 more
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The dissipative sine-Gordon equation
Foundations of Physics Letters, 1996Application of the decomposition method to the generalizations of the sine-Gordon equation provide efficient analytic solution without linearization or perturbation.
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Conservation laws of sine-Gordon equation
Physics Letters A, 1974Abstract It is shown that the conservation laws of the sine-Gordon equation are obtained in the recurrent fashion.
H. Sanuki, K. Konno
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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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Exact solutions of coupled sine–Gordon equations
Nonlinear Analysis: Real World Applications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Conservation Laws in sine-Gordon Equation
Chinese Physics Letters, 2003There are two conservation quantities needed to derive conservation laws of sine-Gordon equation in a frame of laboratory reference. One of them could be derived easily with a standard process, but the other could not. After the gauge transformation e-iθσ2/2 is introduced, we simply obtain the other one without any questionable assumption.
Shi Li-Na +3 more
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