Geodesic
Example of a self-localizing nonlinear relativistic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 100-104

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The real scalar relativistic field with self-interaction $(\lambda/4)\psi^4$ in the Lagrangian is studied. An exact solution is obtained for the one- and three-dimensional cases. It is shown that in the one-dimensional case the field is localized in a certain region whose size varies in accordance with a Lorentz transformation. The energy and momentum of the field are inversely proportional to the coupling constant, and they are related by the same relativistic equation as for a particle with a certain internal energy. In the three-dimensional case the field is localized only in one dimension. 
@article{TMF_1973_16_1_a10,
     author = {A. S. Davydov and N. I. Kislukha},
     title = {Example of a self-localizing nonlinear relativistic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {100--104},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_16_1_a10/}
}
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A. S. Davydov; N. I. Kislukha. Example of a self-localizing nonlinear relativistic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 100-104. http://geodesic.mathdoc.fr/item/TMF_1973_16_1_a10/