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  • 1
    Electronic Resource
    Electronic Resource
    Generalized Skyrme model on higher-dimensional Riemannian manifolds (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 824-828 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Skyrme model is generalized to higher-dimensional Riemannian manifolds and the geometric conditions under which homothetic maps are absolute or local minimizers of the model are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528404
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  • 2
    Electronic Resource
    Electronic Resource
    The Ginzburg–Landau equations for superconducting films and the Meissner effect (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1284-1289 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The existence of the solutions at the lowest energy level to the Ginzburg–Landau equations describing superconducting films under the influence of an external magnetic field is proved. The condition obtained for maintaining superconducting states does not involve the Ginzburg–Landau parameter, and, more surprisingly, in this condition both the external magnetic field and the thickness of the film play equal parts. The asymptotic behavior of these solutions for small or large values of the external field is also studied, which qualitatively verifies the Meissner effect and quantitatively reproduces the solution found from the classical London theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528765
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  • 3
    Electronic Resource
    Electronic Resource
    Existence of the massive SO(3) vortices (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1395-1399 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the massive SO(3) gauge field theory, a critical choice of the configuration ansatz leads to a system of the Bogomol'nyi type equations governing the unstable modes of the model. A 't Hooft periodic condition implies the quantization of the flux lines confined in a cell domain if a certain class of solutions exist. The present paper establishes an existence theorem for such solutions via a constrained variational principle. These solutions exhibit the analogous properties of the vortex-like solutions predicted in the theory of type II superconductivity by Abrikosov.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529292
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  • 4
    Electronic Resource
    Electronic Resource
    Blow-up of the SU(2,C) Yang–Mills fields (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1237-1239 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is remarked that, if the gauge group is not compact, finite−time blowing−up Yang–Mills fields over the Minkowski spaces may exist. The example taken is G=SU(2,C). It is shown that blow−up can occur in an arbitrarily small time interval when the initial data of the fields are suitably chosen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528759
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  • 5
    Electronic Resource
    Electronic Resource
    Skyrme models with self-dual limits: d=2,3 (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2569-2584 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The most general Skyrme–Sigma models in two and three Euclidean dimensions described by O(3) and O(4) fields, respectively, are studied first by numerical methods, and analytic proofs of existence are subsequently given. Particular emphasis is given to the special cases of these models, where the topological inequalities can be saturated by self-duality equations. The O(d+1) models in d dimensions exhibit qualitatively similar features. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531529
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  • 6
    Electronic Resource
    Electronic Resource
    Solutions of the generalized Bogomol'nyi equations via monotone iterations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 4239-4249 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper is concerned with the numerical solutions of the classical Abelian Higgs vortex model in R2 in the critical coupling phase. A globally convergent monotone iterative method will be presented to approximate finite energy multivortex solutions of both the classical and the generalized Bogomol'nyi equations. In the latter context, it is illustrated through a series of numerical examples that the Higgs potential density function may be adjusted to realize in a wide range fairly different magnetic concentration pictures of the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529824
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  • 7
    Electronic Resource
    Electronic Resource
    On the existence of multivortices in a generalized Bogomol'nyi system (1992)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 677-696 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An interesting feature of the generalized Abelian Higgs vortex model introduced by M. Lohe is that it allows a wider class of Higgs self-interaction potential functions, yet, noninteracting multivortices are still present in the critical coupling phase as the solutions of a modified Bogomol'nyi system. In this paper, we add two new classes of multivortex solutions to Lohe's model. We prove that, under the 't Hooft boundary condition, there are solutions realizing a periodic lattice structure and a quantized flux. A necessary and sufficient condition is obtained for the existence of such solutions. We also show that the Meissner effect occurs in the model. Moreover, we establish for any given vortex distribution in the plane, the existence of a one-parameter family of gauge-distinct solutions of infinite energy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946256
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  • 8
    Electronic Resource
    Electronic Resource
    Prescribing topological defects for the coupled Einstein and Abelian Higgs equations (1995)
    Springer
    Communications in mathematical physics 170 (1995), S. 541-582 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct multi-string solutions of the coupled Einstein and Abelian Higgs equations so that the spacetime is uniform along the time axis and a vertical direction and nontrivial geometry is coded on a Riemann surfaceM. We concentrate on the critical Bogomol'nyi phase. WhenM is compact, the Abelian Higgs model is defined by a complex line bundleL overM. We prove that, due to the coupling of the Einstein equations, the Euler characteristic ofM and the first Chern number of the line bundleL identified as the total string number impose an exact obstruction to the existence of a string solution. Such an obstruction leads to some interesting implications. We then study the existence of multi-string solutions which can realize a prescribed string distribution. We show that there are such solutions when the local string winding numbers do not exceed half of the total string number. WhenM is noncompact and globally conformal to a plane, we show that the energy scale of symmetry breaking plays a crucial role and there are finite-energy radially symmetric string solutions realizing a given string number if and only if the symmetry breaking scale is sufficiently small but nonvanishing. Finally, we obtain finite-energy multistring solutions with an arbitrary string distribution and associated local winding numbers. These solutions are not radially symmetric and are regular everywhere and topologically nontrivial so that both the energy of the matter-gauge sector and the energy of the gravitational sector viewed as the total Gauss curvature ofM are quantized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099149
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  • 9
    Electronic Resource
    Electronic Resource
    Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes (1997)
    Springer
    Communications in mathematical physics 188 (1997), S. 737-751 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO ±(4 p) Yang–Mills theory in the Euclidean 4 p (p≥ 2) dimensions allows an axially symmetric self-dual system of equations similar to Witten's instanton equations in the classical 4-dimensional SU(2)∼SO ±(4) theory and the solutions represent a new class of instantons. However the rigorous existence of these higher-dimensional instanton solutions has remained open except for the solution of unit charge representing a single instanton. In this paper we establish an existence and uniqueness theorem for multi-instantons of arbitrary charges in the case p≥ 2. These solutions are the first known instantons, with the Chern–Pontryagin index greater than one, of the Yang–Mills model in higher dimensions. Our approach is a study of a nonlinear variational equation defined on the Poincaré half plane.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050186
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  • 10
    Electronic Resource
    Electronic Resource
    The existence of Solitons in Gauged Sigma Models with Broken Symmetry: Some Remarks (1997)
    Springer
    Letters in mathematical physics 40 (1997), S. 177-189 
    Details
    ISSN: 1573-0530
    Keywords: vortices ; elliptic equations ; monotone method ; shooting.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove the existence of multisolitons in the gauged self-dual Maxwell and Chern–Simons sigma models with broken symmetry. In the context of topological solutions, the existence proofs rely on established results on earlier models. In the context of nontopological solutions with radial symmetry, the proof is by adapting a shooting argument.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007363726173
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