Bubbling solutions for the Chern-Simons gauged \(O(3)\) sigma model on a torus
The authors are concerned with the nonlinear partial differential equation \[ \Delta u+\frac{f_\tau(u)}{\varepsilon^2}=4\pi \sum_{j=1}^{d_1}m_{j,1}\delta_{q_j,1}-4\pi \sum_{j=1}^{d_2}m_{j,2}\delta_{q_j,2}, \] where \(u\) is subject to doubly periodic boundary condition, \(\varepsilon=\sqrt{8/\kappa^2}\) and \(f_\tau(u)=e^u(1-e^u)(\tau+e^u)^{-3}\). The authors study the stability, asymptotic behavior and the existence of multiple nontopological periodic solutions for sufficiently small \(\varepsilon>0\). Bubbling solutions which exhibit concentration phenomena at one point of the domain are also investigated.
scientific article; zbMATH DE number 6494030
scientific article