Solitons in Field Theory and Nonlinear Analysis

By Yong Yang. 2001

594 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/98039a4cdfb2c8bd3b073d11b478c98bcc92cd50

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Citations in the corpus

An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, background): “We refer the reader to [25], [68] and to the monographs [67], [72] for further details and an up to date set of references concerning these applications.”
Classification of blowup limits for SU(3) singular Toda systems (2013, methodology): “MR 98h:58047 Zbl 0874.58093 [Yang 2001] Y. Yang, Solitons in field theory and nonlinear analysis, Springer, New York, 2001.”
Mean Field Equation of Liouville Type with Singular Data: Topological Degree (2015, methodology): “Comm. Partial Differential Equations 16 (1991), no. 8-9, 1223–1253. doi:10.1080/03605309108820797 [12] Caffarelli, L. A.; Yang, Y. S. Vortex condensation in the Chern-Simons Higgs model: an existence theorem.”
Some existence results for the Toda system on closed surfaces (2007, background): “is known as the Toda system, and it arises in the study of non-abelian Chern-Simons theory, see for example [16] or [ 31 ].”
Profile of bubbling solutions to a Liouville system (2009, methodology): “Here we also note that another important extension of the Liouville equation is the Toda system, which is closely related to the non-abelian Chern–Simons theory [15,28].”
Classification and nondegeneracy of SU(n+1) Toda system with singular sources (2011, methodology): “For example, in the Chern-Simons theory, the Liouville equation is related to abelian gauge field theory, while the Toda system is related to nonabelian gauge, see [11], [12], [14], [21], [22], [30], [31], [32], [36], [37] and references therein.”
Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions (2005, background): “See for instance the books [10] and [24] and the references therein.”