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Sine-Gordon equation on the semi-axis

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Abstract

We investigate the sine-Gordon equation utt−uxx+sinu=0 on the semi-axis x>0. We show that boundary conditions of the forms ux(0,t)=c1 cos(u(0,t)/2)+c2 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.

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Authors and Affiliations

  1. Institute of Mathematics, Ural Science Center, Russian Academy of Sciences, Ufa, Russia

    I. T. Khabibullin

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  1. I. T. Khabibullin
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 1, pp. 115–125, January, 1998.

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Khabibullin, I.T. Sine-Gordon equation on the semi-axis. Theor Math Phys 114, 90–98 (1998). https://doi.org/10.1007/BF02557111

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  • DOI: https://doi.org/10.1007/BF02557111

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