Geodesic
Investigation of nonlinear one-dimensional systems by means of the Hamiltonian formalism
Teoretičeskaâ i matematičeskaâ fizika, Tome 76 (1988) no. 2, pp. 199-206

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A method is proposed for investigating the solutions of the weakly perturbed sine–Gordon equation by means of action–angle variables. The Green's function of radiation on the background of many-soliton solutions is calculated in the first approximation in the amplitude. The dynamics of one- and two-soliton solutions is investigated. The Landau–Lifshitz equation (including the nonintegrable modifications) is reduced in a special case to the perturbed sine–Gordon equation. Some solutions are investigated. 
@article{TMF_1988_76_2_a3,
     author = {V. G. Mikhalev},
     title = {Investigation of nonlinear one-dimensional systems by means of the {Hamiltonian} formalism},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {199--206},
     publisher = {mathdoc},
     volume = {76},
     number = {2},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_76_2_a3/}
}
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V. G. Mikhalev. Investigation of nonlinear one-dimensional systems by means of the Hamiltonian formalism. Teoretičeskaâ i matematičeskaâ fizika, Tome 76 (1988) no. 2, pp. 199-206. http://geodesic.mathdoc.fr/item/TMF_1988_76_2_a3/