Local well-posedness and local (in space) regularity results for the complex Korteweg–de Vries equation
This paper is concerned with solutions of the complex Korteweg–de Vries (KdV) equation. We achieve two goals. First, we prove local well-posedness results for the complex KdV equation on a line, in a periodic domain and in a finite domain. These results are in line with the local well-posedness theo...
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| Published in | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 137; no. 1; pp. 203 - 223 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Edinburgh, UK
Royal Society of Edinburgh Scotland Foundation
01.02.2007
Cambridge University Press |
| Subjects | |
| Online Access | Get full text |
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| Abstract | This paper is concerned with solutions of the complex Korteweg–de Vries (KdV) equation. We achieve two goals. First, we prove local well-posedness results for the complex KdV equation on a line, in a periodic domain and in a finite domain. These results are in line with the local well-posedness theory for the real KdV equation. Second, we establish a rigorous connection between the local (in space) regularity of the real part and that of the imaginary part of any solution to the complex KdV equation. This result partly validates the numerical observation that the real and imaginary parts of a singular solution of the complex KdV equation blow up at the same point and at the same time. |
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| AbstractList | This paper is concerned with solutions of the complex Korteweg–de Vries (KdV) equation. We achieve two goals. First, we prove local well-posedness results for the complex KdV equation on a line, in a periodic domain and in a finite domain. These results are in line with the local well-posedness theory for the real KdV equation. Second, we establish a rigorous connection between the local (in space) regularity of the real part and that of the imaginary part of any solution to the complex KdV equation. This result partly validates the numerical observation that the real and imaginary parts of a singular solution of the complex KdV equation blow up at the same point and at the same time. This paper is concerned with solutions of the complex Korteweg-de Vries (KdV) equation. We achieve two goals. First, we prove local well-posedness results for the complex KdV equation on a line, in a periodic domain and in a finite domain. These results are in line with the local well-posedness theory for the real KdV equation. Second, we establish a rigorous connection between the local (in space) regularity of the real part and that of the imaginary part of any solution to the complex KdV equation. This result partly validates the numerical observation that the real and imaginary parts of a singular solution of the complex KdV equation blow up at the same point and at the same time. [PUBLICATION ABSTRACT] |
| Author | Wu, Jiahong Yuan, Juan-Ming |
| Author_xml | – sequence: 1 givenname: Jiahong surname: Wu fullname: Wu, Jiahong email: jiahong@math.okstate.edu organization: Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078, USA (jiahong@math.okstate.edu) – sequence: 2 givenname: Juan-Ming surname: Yuan fullname: Yuan, Juan-Ming email: jmyuan@pu.edu.tw organization: Department of Applied Mathematics, Providence University, 200 Chung-Chi Road, Shalu 433, Taichung Hsien, Taiwan, Republic of China (jmyuan@pu.edu.tw) |
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| Snippet | This paper is concerned with solutions of the complex Korteweg–de Vries (KdV) equation. We achieve two goals. First, we prove local well-posedness results for... This paper is concerned with solutions of the complex Korteweg-de Vries (KdV) equation. We achieve two goals. First, we prove local well-posedness results for... |
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| Title | Local well-posedness and local (in space) regularity results for the complex Korteweg–de Vries equation |
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