Khabibullin, I. T. 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. Cited in 5 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems Keywords:sine-Gordon equation; boundary conditions; Bäcklund transformation; multisoliton solution PDF BibTeX XML Cite \textit{I. T. Khabibullin}, Theor. Math. Phys. 114, No. 1, 90--98 (1998; Zbl 0946.35089); translation from Teor. Mat. Fiz. 114, No. 1, 115--125 (1998) Full Text: DOI References: [1] I. T. Khabibullin (Habibullin),Nonlinear Math. Phys.,3, No. 1-2, 147–151 (1996). · Zbl 1044.35521 · doi:10.2991/jnmp.1996.3.1-2.16 [2] V. Adler, B. Gürel, V. Gürses, and I. Khabibullin (Habibullin)J. Phys. A,30, 3505–3513 (1997). · Zbl 0927.35093 · doi:10.1088/0305-4470/30/10/025 [3] S. Ghoshal and A. B. Zamolodchikov, ”Boundary state and boundaryS-matrix two-dimensional integrable field theory,” Preprint Rutgers University RU-93-20; hep-th/9306002. · Zbl 0985.81714 [4] E. Corrigan, P. E. Dorey, R. H. Rietdijk, and R. Sasaki, ”Affine Toda field theory on a half-line”, hep-th/9404108. · Zbl 0868.35115 [5] H. Saleur, S. Skorik, and N. P. Warner, ”The boundary sine-Gordon theory,” Preprint USC-94-013; hep-th/9408004. · Zbl 0990.81705 [6] E. K. Sklyanin,Funct. Anal. Appl.,21, No. 2, 164–166 (1987). · Zbl 0643.35093 · doi:10.1007/BF01078038 [7] I. T. Khabibullin (Habibullin),Theor. Math. Phys.,86, 28–35 (1991). · Zbl 0728.35114 · doi:10.1007/BF01018494 [8] V. O. Tarasov,Inverse Problems,7, 435–449 (1991). · Zbl 0732.35089 · doi:10.1088/0266-5611/7/3/009 [9] R. F. Bikbaev and V. O. Tarasov,Algebra Anal.,3, No. 4, 78–92 (1991). [10] V. E. Adled, I. T. Khabibullin (Habibullin), and A. B. Shabat,Theor. Math. Phys.,110, 78–90 (1997). · Zbl 0916.35100 · doi:10.1007/BF02630371 [11] A. P. Veselov and A. B. Shabat,Funct. Anal. Appl.,27, No. 2, 81–96 (1993). · Zbl 0813.35099 · doi:10.1007/BF01085979 [12] L. A. Takhtajan and L. D. Faddeev,Hamiltonian Approach in the Theory of Solitons, Springer, Berlin-Heidelberg-New York (1987). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.