Relativistic Chern-Simons-Higgs vortex equations (Q2790600)

The principal object of study considered in this work is a nonlinear generalization of the stationary Toda lattice formed by diffusively coupled elements, where arguments of its additive non-linear terms are \(u_j\) and \(u_j+u_k\). Here \(j\) and \(k\) are indices of elements. These additional terms, which depend on the sum of components, result in a more complicated analytical structure for the considered differential equation. The main result is the theorem, which determines constraints on the multiplier at the non-linear part for an existence of a solution, as well as asymptotic and integral estimations of the latter.