Existence of string-like solitons (Q1809075)

The paper is devoted to solitons in three space dimensions. A soliton is a solution of a field equation whose energy travels as a localized packet and which preserves its form under perturbations. The authors consider the energy functional \[ E(u)= \int_{\mathbb{R}^3} |\nabla u|^2 dx+ \frac{\varepsilon^4}{6} \int_{\mathbb{R}^3} |\nabla u|^6 dx \] and obtain a field equation for which it is possible to prove the existence of string-like solitons.