Construction of some classes of nonlinear PDE’s admitting soliton solutions
Volume 523 / 2017
Dissertationes Mathematicae 523 (2017), 1-98
MSC: 35C07, 35C08, 35D30, 35J30, 35J35, 35J50, 35J60, 35Q31, 35Q51, 46E35, 47H11.
DOI: 10.4064/dm752-7-2016
Published online: 7 June 2017
Abstract
We study a class of Lorentz invariant nonlinear field equations in multiple space dimensions. The main purpose is to obtain soliton-like solutions with variable exponent. The fields are characterized by a topological invariant, which we call the charge. We prove the existence of a static solution which minimizes the energy among the configurations with nontrivial charge.
