Geodesic
Asymptotic solitons of~the sine-Gordon equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 15-28

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The large time asymptotics of the solutions of the sine-Gordon equation which tend to zero when $x\to\infty$ and tend to the finite-gap solution of this equation when $x\to-\infty$ are investigated. It is proved that at $t\to\infty$ these solutions split into infinite series of solitons with variable phases. These solitons are generated by the continuous spectrum of the $L$-operator from the corresponding Lax representation. 
@article{TMF_1989_80_1_a1,
     author = {V. P. Kotlyarov},
     title = {Asymptotic solitons of~the {sine-Gordon} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {15--28},
     publisher = {mathdoc},
     volume = {80},
     number = {1},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a1/}
}
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V. P. Kotlyarov. Asymptotic solitons of~the sine-Gordon equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 15-28. http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a1/