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This article is cited in 7 scientific papers (total in 7 papers)
Sine-Gordon equation on the semi-axis
I. T. Habibullin
Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Abstract:
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.
DOI:
https://doi.org/10.4213/tmf832
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English version:
Theoretical and Mathematical Physics, 1998, 114:1, 90–98
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Received: 11.08.1997
Citation:
I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, TMF, 114:1 (1998), 115–125; Theoret. and Math. Phys., 114:1 (1998), 90–98
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 1998
\vol 114
\issue 1
\pages 90--98
\crossref{https://doi.org/10.1007/BF02557111}
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http://mi.mathnet.ru/eng/tmf832https://doi.org/10.4213/tmf832 http://mi.mathnet.ru/eng/tmf/v114/i1/p115
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Kundu, A, “Changing Solitons in Classical & Quantum Integrable Defect and Variable Mass sine-Gordon Model”, Journal of Nonlinear Mathematical Physics, 15 (2008), 237
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Habibullin, I, “Quantum and classical integrable sine-Gordon model with defect”, Nuclear Physics B, 795:3 (2008), 549
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Corrigan E. Zambon C., “Infinite Dimension Reflection Matrices in the sine-Gordon Model with a Boundary”, J. High Energy Phys., 2012, no. 6, 050
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Aguirre A.R. Gomes J.F. Ymai L.H. Zimerman A.H., “N=1 Super Sinh-Gordon Model in the Half Line: Breather Solutions”, J. High Energy Phys., 2013, no. 4, 136
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