Geodesic
Sine-Gordon equation on the semi-axis
Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 1, pp. 115-125

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We investigate the sine-Gordon equation $u_{tt}-u_{xx}+\sin u=0$ on the semi-axis $x>0$. We show that boundary conditions of the forms $u_x(0,t)=c_1\cos(u(0,t)/2)+ c_2\sin(u(0,t)/2)$ and $u(0,t)=c$ are compatible with the Bдcklund transformation. We construct a multisoliton solution satisfying these boundary conditions. 
@article{TMF_1998_114_1_a5,
     author = {I. T. Habibullin},
     title = {Sine-Gordon equation on the semi-axis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {115--125},
     publisher = {mathdoc},
     volume = {114},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a5/}
}
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I. T. Habibullin. Sine-Gordon equation on the semi-axis. Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 1, pp. 115-125. http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a5/