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Sine-Gordon equation on the semi-axis. (English. Russian original) Zbl 0946.35089
Theor. Math. Phys. 114, No. 1, 90-98 (1998); translation from Teor. Mat. Fiz. 114, No. 1, 115-125 (1998).
Summary: 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 form \(u_x(0,t)= c_1\cos (u(0,t)/2) +c_2\sin (u(0,t)/2)\) and \(u(0,t)=c\) are compatible with the Bäcklund transformation. We construct a multisoliton solution satisfying these boundary conditions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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