Editing Soliton (section)

==Bions==

The bound state of two solitons is known as a ''bion'',<ref>{{Cite journal|last1=Belova|first1=T.I.|last2=Kudryavtsev|first2=A.E.|year=1997|title=Solitons and their interactions in classical field theory|journal=Physics-Uspekhi|volume=40|issue=4|pages=359–386|doi=10.1070/pu1997v040n04abeh000227|bibcode=1997PhyU...40..359B|s2cid=250768449 }}</ref><ref>{{Cite journal|last1=Gani|first1=V.A.|last2=Kudryavtsev|first2=A.E.|last3=Lizunova|first3=M.A.|year=2014|title=Kink interactions in the (1+1)-dimensional φ^6 model|journal=Physical Review D|volume=89|issue=12|pages=125009|doi=10.1103/PhysRevD.89.125009|arxiv=1402.5903|bibcode=2014PhRvD..89l5009G|s2cid=119333950}}</ref><ref>{{Cite journal|last1=Gani|first1=V.A.|last2=Lensky|first2=V.|last3=Lizunova|first3=M.A.|year=2015|title=Kink excitation spectra in the (1+1)-dimensional φ^8 model|journal=Journal of High Energy Physics|language=en|volume=2015|issue=8|pages=147|arxiv=1506.02313|doi=10.1007/JHEP08(2015)147|s2cid=54184500|issn=1029-8479}}</ref><ref name=":0">{{Cite journal|last=Khazali|first=Mohammadsadegh|date=2021-08-05|title=Rydberg noisy dressing and applications in making soliton molecules and droplet quasicrystals|url=https://link.aps.org/doi/10.1103/PhysRevResearch.3.L032033|journal=Physical Review Research|volume=3|issue=3|pages=L032033|doi=10.1103/PhysRevResearch.3.L032033|arxiv=2007.01039|bibcode=2021PhRvR...3c2033K |s2cid=220301701 }}</ref> or in systems where the bound state periodically oscillates, a ''[[breather]]''. The interference-type forces between solitons could be used in making bions.<ref>{{Cite journal|last1=Nguyen|first1=Jason H. V.|last2=Dyke|first2=Paul|last3=Luo|first3=De|last4=Malomed|first4=Boris A.|last5=Hulet|first5=Randall G.|date=2014-11-02|title=Collisions of matter-wave solitons|url=http://dx.doi.org/10.1038/nphys3135|journal=Nature Physics|volume=10|issue=12|pages=918–922|doi=10.1038/nphys3135|issn=1745-2473|arxiv=1407.5087|bibcode=2014NatPh..10..918N |s2cid=85461409 }}</ref> However, these forces are very sensitive to their relative phases. Alternatively, the bound state of solitons could be formed by dressing atoms with highly excited Rydberg levels.<ref name=":0" /> The resulting self-generated potential profile<ref name=":0" /> features an inner attractive soft-core supporting the 3D self-trapped soliton, an intermediate repulsive shell (barrier) preventing solitons’ fusion, and an outer attractive layer (well) used for completing the bound state resulting in giant stable soliton molecules. In this scheme, the distance and size of the individual solitons in the molecule can be controlled dynamically with the laser adjustment.

In field theory ''bion'' usually refers to the solution of the [[Born–Infeld model]]. The name appears to have been coined by G. W. Gibbons in order to distinguish this solution from the conventional soliton, understood as a ''regular'', finite-energy (and usually stable) solution of a differential equation describing some physical system.<ref>{{cite journal | title=Born–Infeld particles and Dirichlet ''p''-branes | first=G. W. | last=Gibbons | volume=514 | issue=3 | year=1998 | pages=603–639 | doi=10.1016/S0550-3213(97)00795-5 | journal=Nuclear Physics B |arxiv = hep-th/9709027 |bibcode = 1998NuPhB.514..603G | s2cid=119331128 }}</ref> The word ''regular'' means a smooth solution carrying no sources at all. However, the solution of the Born–Infeld model still carries a source in the form of a Dirac-delta function at the origin. As a consequence it displays a singularity in this point (although the electric field is everywhere regular). In some physical contexts (for instance string theory) this feature can be important, which motivated the introduction of a special name for this class of solitons.

On the other hand, when gravity is added (i.e. when considering the coupling of the Born–Infeld model to general relativity) the corresponding solution is called ''EBIon'', where "E" stands for Einstein.