Results 221 to 230 of about 1,104 (261)
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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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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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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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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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The sine-Gordon equation in the finite line
Applied Mathematics and Computation, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An ultradiscretization of the sine-Gordon equation
Physics Letters A, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Isojima, S. +3 more
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International Journal of Computer Mathematics, 2010
We present an efficient modification of the He's homotopy perturbation method that will facilitate the calculations. We apply this modification to solve sine-Gordon and coupled sine-Gordon equations, numerically. The new modification introduces a promising tool for many non-linear problems.
Mohammad Taghi Darvishi +3 more
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We present an efficient modification of the He's homotopy perturbation method that will facilitate the calculations. We apply this modification to solve sine-Gordon and coupled sine-Gordon equations, numerically. The new modification introduces a promising tool for many non-linear problems.
Mohammad Taghi Darvishi +3 more
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The sine-Gordon Equation of a Dislocation
2020The distances between the points of a lattice make up a characteristic length for the properties of a dislocation.
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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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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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