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Integrability of potentials of degree $k \neq \pm 2$. Second order variational equations between Kolchin solvability and Abelianity
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Radial stability of periodic solutions of the Gylden-Meshcherskii-type problem
Topological defects in the abelian Higgs model
1. | Department of Mathematical Sciences, Binghamton University (SUNY), Binghamton, NY 13902-6000 |
2. | Department of Mathematics, University of Toronto, Bahen Centre 40 St. George St., Room 6290, Toronto, ON M5S 2E4, Canada |
References:
[1] |
Y. Almog, L. Berlyand, D. Golovaty and I. Shafrir, Global minimizers for a $p$-Ginzburg-Landau-type energy in $\mathbbR^2$,, J. Funct. Anal., 256 (2009), 2268.
doi: 10.1016/j.jfa.2008.09.020. |
[2] |
G. Bellettini, J. Hoppe, M. Novaga and G. Orlandi, Closure and convexity results for closed relativistic strings,, Complex Anal. Oper. Theory, 4 (2010), 473.
doi: 10.1007/s11785-010-0060-y. |
[3] |
G. Bellettini, M. Novaga and G. Orlandi, Time-like minimal submanifolds as singular limits of nonlinear wave equations,, Phys. D, 239 (2010), 335.
doi: 10.1016/j.physd.2009.12.004. |
[4] |
M. S. Berger and Y. Y. Chen, Symmetric vortices for the Ginzburg-Landau equations of superconductivity and the nonlinear desingularization phenomenon,, J. Funct. Anal., 82 (1989), 259.
doi: 10.1016/0022-1236(89)90071-2. |
[5] |
P. Goddard, From Dual Models to String Theory,, The birth of string theory, (2012).
|
[6] |
T. Gotô, Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary conditon of dual resonance model,, Progr. Theoret. Phys., 46 (1971), 1560.
doi: 10.1143/PTP.46.1560. |
[7] |
S. Gustafson and I. M. Sigal, The stability of magnetic vortices,, Comm. Math. Phys., 212 (2000), 257.
doi: 10.1007/PL00005526. |
[8] |
S. Gustafson and I. M. Sigal, Effective dynamics of magnetic vortices,, Adv. Math., 199 (2006), 448.
doi: 10.1016/j.aim.2005.05.017. |
[9] |
A. Jaffe and C. Taubes, Vortices and Monopoles, vol. 2 of Progress in Physics,, Birkhäuser Boston, (1980).
|
[10] |
R. L. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals,, SIAM J. Math. Anal., 30 (1999), 721.
doi: 10.1137/S0036141097300581. |
[11] |
R. L. Jerrard, Vortex dynamics for the Ginzburg-Landau wave equation,, Calc. Var. Partial Differential Equations, 9 (1999), 1.
doi: 10.1007/s005260050131. |
[12] |
R. Jerrard, Defects in semilinear wave equations and timelike minimal surfaces in Minkowski space,, Anal. PDE, 4 (2011), 285.
doi: 10.2140/apde.2011.4.285. |
[13] |
R. Jerrard, M. Novaga and G. Orlandi, On the regularity of timelike extremal surfaces,, To appear, ().
doi: 10.1142/S0219199714500485. |
[14] |
M. Keel, Global existence for critical power Yang-Mills-Higgs equations in $R^{3+1}$,, Comm. Partial Differential Equations, 22 (1997), 1161.
|
[15] |
T. W. B. Kibble, Topology of cosmic domains and strings,, Journal of Physics A: Mathematical and General, 9 (1976).
doi: 10.1088/0305-4470/9/8/029. |
[16] |
S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy,, Duke Math. J., 74 (1994), 19.
doi: 10.1215/S0012-7094-94-07402-4. |
[17] |
F. H. Lin, Vortex dynamics for the nonlinear wave equation,, Comm. Pure Appl. Math., 52 (1999), 737.
doi: 10.1002/(SICI)1097-0312(199906)52:6<737::AID-CPA3>3.0.CO;2-Y. |
[18] |
Y. Nambu, Duality and Hadrodynamics (Notes prepared for the Copenhagen High Energy Symposium, unpublished, 1970), Broken symmetry, vol. 13 of World Scientific Series in 20th Century Physics,, World Scientific Publishing Co. Inc., (1995).
|
[19] |
L. Nguyen and G. Tian, On the smoothness of timelike maximal cylinders in three dimensional vacuum spacetimes,, Classical Quantum Gravity, 30 (2013).
doi: 10.1088/0264-9381/30/16/165010. |
[20] |
H. B. Nielsen and P. Olesen, Vortex-line models for dual strings,, Nuclear Phys., 61 (1973), 45.
doi: 10.1016/0550-3213(73)90350-7. |
[21] |
T. Rivière, Towards Jaffe and Taubes conjectures in the strongly repulsive limit,, Manuscripta Math., 108 (2002), 217.
doi: 10.1007/s002290200266. |
[22] |
E. Sandier and S. Serfaty, Vortices in the Magnetic Ginzburg-Landau Model,, Progress in Nonlinear Differential Equations and their Applications, (2007).
|
[23] |
S. Selberg and A. Tesfahun, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge,, Comm. Partial Differential Equations, 35 (2010), 1029.
doi: 10.1080/03605301003717100. |
[24] |
D. Stuart, Dynamics of abelian Higgs vortices in the near Bogomolny regime,, Comm. Math. Phys., 159 (1994), 51.
doi: 10.1007/BF02100485. |
[25] |
D. M. A. Stuart, The geodesic hypothesis and non-topological solitons on pseudo-Riemannian manifolds,, Ann. Sci. École Norm. Sup. (4), 37 (2004), 312.
doi: 10.1016/j.ansens.2003.07.001. |
[26] |
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects,, Cambridge Monographs on Mathematical Physics, (1994).
|
[27] |
Y. Yu, Vortex dynamics for the nonlinear Maxwell-Klein-Gordon equation,, Arch. Ration. Mech. Anal., 201 (2011), 743.
doi: 10.1007/s00205-011-0422-2. |
show all references
References:
[1] |
Y. Almog, L. Berlyand, D. Golovaty and I. Shafrir, Global minimizers for a $p$-Ginzburg-Landau-type energy in $\mathbbR^2$,, J. Funct. Anal., 256 (2009), 2268.
doi: 10.1016/j.jfa.2008.09.020. |
[2] |
G. Bellettini, J. Hoppe, M. Novaga and G. Orlandi, Closure and convexity results for closed relativistic strings,, Complex Anal. Oper. Theory, 4 (2010), 473.
doi: 10.1007/s11785-010-0060-y. |
[3] |
G. Bellettini, M. Novaga and G. Orlandi, Time-like minimal submanifolds as singular limits of nonlinear wave equations,, Phys. D, 239 (2010), 335.
doi: 10.1016/j.physd.2009.12.004. |
[4] |
M. S. Berger and Y. Y. Chen, Symmetric vortices for the Ginzburg-Landau equations of superconductivity and the nonlinear desingularization phenomenon,, J. Funct. Anal., 82 (1989), 259.
doi: 10.1016/0022-1236(89)90071-2. |
[5] |
P. Goddard, From Dual Models to String Theory,, The birth of string theory, (2012).
|
[6] |
T. Gotô, Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary conditon of dual resonance model,, Progr. Theoret. Phys., 46 (1971), 1560.
doi: 10.1143/PTP.46.1560. |
[7] |
S. Gustafson and I. M. Sigal, The stability of magnetic vortices,, Comm. Math. Phys., 212 (2000), 257.
doi: 10.1007/PL00005526. |
[8] |
S. Gustafson and I. M. Sigal, Effective dynamics of magnetic vortices,, Adv. Math., 199 (2006), 448.
doi: 10.1016/j.aim.2005.05.017. |
[9] |
A. Jaffe and C. Taubes, Vortices and Monopoles, vol. 2 of Progress in Physics,, Birkhäuser Boston, (1980).
|
[10] |
R. L. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals,, SIAM J. Math. Anal., 30 (1999), 721.
doi: 10.1137/S0036141097300581. |
[11] |
R. L. Jerrard, Vortex dynamics for the Ginzburg-Landau wave equation,, Calc. Var. Partial Differential Equations, 9 (1999), 1.
doi: 10.1007/s005260050131. |
[12] |
R. Jerrard, Defects in semilinear wave equations and timelike minimal surfaces in Minkowski space,, Anal. PDE, 4 (2011), 285.
doi: 10.2140/apde.2011.4.285. |
[13] |
R. Jerrard, M. Novaga and G. Orlandi, On the regularity of timelike extremal surfaces,, To appear, ().
doi: 10.1142/S0219199714500485. |
[14] |
M. Keel, Global existence for critical power Yang-Mills-Higgs equations in $R^{3+1}$,, Comm. Partial Differential Equations, 22 (1997), 1161.
|
[15] |
T. W. B. Kibble, Topology of cosmic domains and strings,, Journal of Physics A: Mathematical and General, 9 (1976).
doi: 10.1088/0305-4470/9/8/029. |
[16] |
S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy,, Duke Math. J., 74 (1994), 19.
doi: 10.1215/S0012-7094-94-07402-4. |
[17] |
F. H. Lin, Vortex dynamics for the nonlinear wave equation,, Comm. Pure Appl. Math., 52 (1999), 737.
doi: 10.1002/(SICI)1097-0312(199906)52:6<737::AID-CPA3>3.0.CO;2-Y. |
[18] |
Y. Nambu, Duality and Hadrodynamics (Notes prepared for the Copenhagen High Energy Symposium, unpublished, 1970), Broken symmetry, vol. 13 of World Scientific Series in 20th Century Physics,, World Scientific Publishing Co. Inc., (1995).
|
[19] |
L. Nguyen and G. Tian, On the smoothness of timelike maximal cylinders in three dimensional vacuum spacetimes,, Classical Quantum Gravity, 30 (2013).
doi: 10.1088/0264-9381/30/16/165010. |
[20] |
H. B. Nielsen and P. Olesen, Vortex-line models for dual strings,, Nuclear Phys., 61 (1973), 45.
doi: 10.1016/0550-3213(73)90350-7. |
[21] |
T. Rivière, Towards Jaffe and Taubes conjectures in the strongly repulsive limit,, Manuscripta Math., 108 (2002), 217.
doi: 10.1007/s002290200266. |
[22] |
E. Sandier and S. Serfaty, Vortices in the Magnetic Ginzburg-Landau Model,, Progress in Nonlinear Differential Equations and their Applications, (2007).
|
[23] |
S. Selberg and A. Tesfahun, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge,, Comm. Partial Differential Equations, 35 (2010), 1029.
doi: 10.1080/03605301003717100. |
[24] |
D. Stuart, Dynamics of abelian Higgs vortices in the near Bogomolny regime,, Comm. Math. Phys., 159 (1994), 51.
doi: 10.1007/BF02100485. |
[25] |
D. M. A. Stuart, The geodesic hypothesis and non-topological solitons on pseudo-Riemannian manifolds,, Ann. Sci. École Norm. Sup. (4), 37 (2004), 312.
doi: 10.1016/j.ansens.2003.07.001. |
[26] |
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects,, Cambridge Monographs on Mathematical Physics, (1994).
|
[27] |
Y. Yu, Vortex dynamics for the nonlinear Maxwell-Klein-Gordon equation,, Arch. Ration. Mech. Anal., 201 (2011), 743.
doi: 10.1007/s00205-011-0422-2. |
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