Soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method |
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Authors: | Yong Zhang Yanwei Ren Huanhe Dong |
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Affiliation: | 1.College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;2.College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China |
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Abstract: | In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background. Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time $t$ is large, then we give the comparison between the exact solution and the asymptotic solution. |
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Keywords: | robust inverse scattering method modified Korteweg–de Vries equation soliton solution rational travelling waves asymptotic analysis |
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