Geodesic
Conoidal waves in the $\varphi^4$ model with self-interacting currents
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 469-476 
V. E. Grishin; V. K. Fedyanin. Conoidal waves in the $\varphi^4$ model with self-interacting currents. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 469-476. http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a15/
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     author = {V. E. Grishin and V. K. Fedyanin},
     title = {Conoidal waves in the~$\varphi^4$ model with self-interacting currents},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {469--476},
     year = {1983},
     volume = {54},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new form of solutions for relativistic wave equations in the form of rotating “conoidal” waves is found and studied. These waves are more general solutions of periodic type. These essentially nonlinear waves, expressed in terms of elliptic functions, include as special cases nonperiodic solutions of soliton type. In a limiting case, the nonlinear waves can go over into linear oscillations, forming a vacuum condensate.

[1] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR | Zbl

[2] Krylov N. M., Bogolyubov N. N., Vvedenie v nelineinuyu mekhaniku, izd-vo AN USSR, Kiev, 1973

[3] Grishin V. E., Fedyanin V. K., Preprint R17-81-659, OIYaI, Dubna, 1981

[4] Abramowitz M. A., Stegan I. A., Handbook of Mathematical Functions, National Bureau of Standards, Washington, 1964 | MR