On some Lagrangian model concerning the solitary waves. (English) Zbl 0813.58027
Summary: The purpose of this paper is to apply Finsler’s geometric ideas to formulate the field theory containing solitons as solutions of the field equations. Moreover, the connections with the Lax representation of soliton equations and with the Kadomtsev-Petviashvili system are shown.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 35Q51 | Soliton equations |
| 58B20 | Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds |
| 58Z05 | Applications of global analysis to the sciences |
Keywords:
Finsler geometry; field theory; solitons; Lax representation; Kadomtsev- Petviashvili systemReferences:
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