Soliton Asymptotics of Solutions of the Sine-Gordon Equation |
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Authors: | Werner Kirsch Vladimir Kotlyarov |
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Affiliation: | (1) Institute of Mathematics of the Ruhr-University Bochum, D-44780 Bochum, Germany;(2) Mathematical Division, B. Verkin Institute for Low Temperature Physics, 310164 Kharkov, Ukraine |
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Abstract: | An asymptotic analysis of the Marchenko integral equation for the sine-Gordon equation is presented. The results are used for a construction of soliton asymptotics of decreasing and some non-decreasing solutions of the sine-Gordon equation. The soliton phases are shown to have an additional shift with respect to the reflectionless case caused by the non-zero reflection coefficient of the corresponding Dirac operator. Explicit formulas for the phases are also obtained. The results demonstrate an interesting phenomenon of splitting of non-decreasing solutions into an infinite series of asymptotic solitons. |
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Keywords: | solitons sine-Gordon equation Marchenko equation |
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