Standing waves of nonlinear Schrödinger equations with the gauge field

By Jaeyoung Byeon, Hyungjin Huh, Jinmyoung Seok. 2012

142 citations recorded by the source corpus.

Abstract We study standing waves for nonlinear Schrodinger equations with the gauge field. Some existence results of standing waves are established by applying variational methods to the functional which is obtained by representing the gauge field A μ in terms of complex scalar field ϕ. We also show that there exists no standing wave for certain range of parameters by establishing a new inequality of Sobolev type.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/477f6bd32cb096fb14910c6383ebf6604f955cba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Xiaoyutao Luo
2. Gongbao Li
3. Alessio Pomponio
4. D. Ruiz
5. Xianhua Tang
6. Nikolaos S. Papageorgiou
7. Sitong Chen
8. Vicentiu D. Rădulescu

In Mathematical Physics

1. Xiaoyutao Luo
2. Gongbao Li
3. Alessio Pomponio
4. D. Ruiz
5. Xianhua Tang
6. Sitong Chen
7. Hongyu Ye
8. Huan-Song Zhou

Citations in the corpus

• Boundary concentration of a Gauged nonlinear Schrödinger equation on large balls (2013, methodology): “BOUNDARY CONCENTRATION OF A GAUGED NONLINEAR SCHRÖDINGER EQUATION 5 This was proved in [5] for the problem set in R(2); the same arguments apply to our case.”
• Normalized solutions for the Chern–Simons–Schrödinger equation in R^2 (2017, methodology): “3 in this paper can also be viewed as a complement of the main results in [10, 17].”