9,545 research outputs found

    Stationary axisymmetric solutions of five dimensional gravity

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    We consider stationary axisymmetric solutions of general relativity that asymptote to five dimensional Minkowski space. It is known that this system has a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers-Perry black hole starting from the Schwarzschild solution in five dimensions.Comment: 31 pages, LaTeX; references adde

    Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

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    We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lam\'e equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy

    Discrete Breathers in a Nonlinear Polarizability Model of Ferroelectrics

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    We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its non-dimensionalized Hamiltonian form and its linear spectrum is examined. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises.Comment: 9 pages, 7 figures, 1 tabl

    Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

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    Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that the effective Peierls-Nabarro barrier potential is nonzero thereby indicating that this discrete model is quite likely nonintegrable
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