Solitone solutions complexifications of the Korteweg - de Vriz equation
The Hirota method for construction of soliton solutions is applied to the complexification of the Korteweg-de Vries equation. To use the method, the complex equation is replaced by a system of two third-order equations into two real functions, which, using the Hirota differential operator, is reduce...
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| Main Author: | |
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| Format: | Article |
| Language: | Russian |
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North-Caucasus Federal University
2022-09-01
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| Series: | Наука. Инновации. Технологии |
| Subjects: | |
| Online Access: | https://scienceit.elpub.ru/jour/article/view/198 |
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| Summary: | The Hirota method for construction of soliton solutions is applied to the complexification of the Korteweg-de Vries equation. To use the method, the complex equation is replaced by a system of two third-order equations into two real functions, which, using the Hirota differential operator, is reduced to a bilinear form that is quadratic in the functions considered. The existence of a one-soliton solution is proved, the real part of which has the form of a soliton, and the imaginary part is a kink. It is proved that the use of the classical perturbation theory approach does not make it possible to construct a two-soliton solution. A special connection between unknown functions is found, which made it possible to reduce the system to a single bilinear equation for which a two-soliton solution is constructed. It is shown that the obtained Hirota polynomial does not satisfy the required properties, which led to the impossibility of constructing a three-soliton solution. |
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| ISSN: | 2308-4758 |