Adam, ChristophNaya Rodríguez, CarlosOleś, KatarzynaRomańczukiewicz, TomaszSánchez Guillén, JoaquínWereszczynski, Andrzej2021-01-182021-01-182020Phys. Rev. D 102, 1050072470-0010http://hdl.handle.net/10347/24215We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., Rn, but they cannot be placed in any finite volume because the resulting formal solutions have infinite energy. Therefore, these objects are interpreted as totally incompressible solitons. As a first particular example, we consider (1+1)-dimensional kinks in theories with a nonstandard kinetic term or, equivalently, in models with the so-called runaway (or vacuumless) potentials. But incompressible solitons also exist in higher dimensions. As specific examples, in (3+1) dimensions we study Skyrmions in the dielectric extensions of both the minimal and BPS Skyrme models. In the latter case, the Skyrmionic matter describes a completely incompressible topological perfect fluideng© 2020 authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAPAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/journal article10.1103/PhysRevD.102.1050072470-0029open access