相关论文: Sine-Gordon equation in higher dimensions: A fresh…
The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its soliton solutions are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these…
Contrary to the common understanding, the Sine-Gordon equation in (1+2) dimensions does have N-soliton solutions for any N. The Hirota algorithm allows for the construction of static N-soliton solutions (i.e., solutions that do not depend…
The Sine-Gordon equation in (1+2) dimensions has N-soliton solutions that propagate at velocities that are lower than the speed of light (c = 1), for any N greater tha or equal to 1. A first integral of the equation, which vanishes…
Contrary to the decades-old understanding, SGn, the Sine-Gordon equation in (1+n) dimensions, has N-soliton solutions for any N >= 1, not only for n = 1, but also for n = 2 and 3. While SG1 solitons are confined to a line, SG2- and…
The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…
We formulate and discuss integrable analogue of the sine-Gordon equation on arbitrary time scales. This unification contains the sine-Gordon equation, discrete sine-Gordon equation and the Hirota equation (doubly discrete sine-Gordon…
Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N greater than or equal to 1. Based on these solutions, a…
Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may…
Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are…
The Hirota transformation for the soliton solutions of the classical Sine-Gordon equation is suggestive of an extremely simple way for the construction of a nonlinear quantum-dynamical system of spin 1/2 particles that is equivalent to the…
The generalized sine-Gordon (sG) equation $u_{tx}=(1+\nu\partial_x^2)\sin\,u$ was derived as an integrable generalization of the sG equation. In a previous paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is referred to…
Employing the Hirota's method, a class of soliton solutions for the N=2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N=1 supersymmetric mKdV equations connected…
In this paper we study the dynamics of explicit solutions of $2+1$-dimensional ($2$D) sine-Gordon equation. The Darboux transformation is applied to the associated linear eigenvalue problem to construct nontrivial solutions of $2$D…
The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the…
Integrable discretizations of the sine-Gordon equation in characteristic (or light-cone) coordinates have been extensively studied after the seminal works of Hirota and Orfanidis in the late 1970s. In contrast, integrable discretizations of…
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…
Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological…
The (2+1)-dimension Klein-Gordon generalised equation is numerically solved through the finite differences method. Only the sine-Gordon case is focused: kink and antikink solutions are obtained in cartesian coordinates and evidence of…
The multi-soliton solution of the sine-Gordon equation in the presence of elliptic-function background is derived by the inverse scattering method. The key tool in our formulation is the Lax pair written by $4\times4$ matrix differential…
We investigate the classical and nonclassical reductions of the $2+1$-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalisation of the sine-Gordon equation. A family of solutions obtained as a nonclassical…