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arXiv · 1305.3076

Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions

Ying-ying Sun·Juan-ming Yuan·Da-jun Zhang
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Abstract

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Korteweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the complex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.

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Ying-ying Sun, Juan-ming Yuan, Da-jun Zhang. 2013-05-14. Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions. https://doi.org/10.1088/0253-6102%2F61%2F4%2F03

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