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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
North-Caucasus Federal University
2022-09-01
|
| Series: | Наука. Инновации. Технологии |
| Subjects: | |
| Online Access: | https://scienceit.elpub.ru/jour/article/view/198 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849388030889033728 |
|---|---|
| author | Tatyana Valentinovna Redkina |
| author_facet | Tatyana Valentinovna Redkina |
| author_sort | Tatyana Valentinovna Redkina |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-debf5c336df34f95a80d2c33a3f2bf69 |
| institution | Kabale University |
| issn | 2308-4758 |
| language | Russian |
| publishDate | 2022-09-01 |
| publisher | North-Caucasus Federal University |
| record_format | Article |
| series | Наука. Инновации. Технологии |
| spelling | doaj-art-debf5c336df34f95a80d2c33a3f2bf692025-08-20T03:42:25ZrusNorth-Caucasus Federal UniversityНаука. Инновации. Технологии2308-47582022-09-01026174197Solitone solutions complexifications of the Korteweg - de Vriz equationTatyana Valentinovna Redkina0North-Caucasus Federal UniversityThe 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.https://scienceit.elpub.ru/jour/article/view/198равнения в частных производныхметод хиротыточные решения нелинейных уравнений в частных производныхсоли-тоныавтомодельное решениеpartial differential equationshirota methodexact solutions of nonlinear partial differential equationssolitonsself-similar solution |
| spellingShingle | Tatyana Valentinovna Redkina Solitone solutions complexifications of the Korteweg - de Vriz equation Наука. Инновации. Технологии равнения в частных производных метод хироты точные решения нелинейных уравнений в частных производных соли-тоны автомодельное решение partial differential equations hirota method exact solutions of nonlinear partial differential equations solitons self-similar solution |
| title | Solitone solutions complexifications of the Korteweg - de Vriz equation |
| title_full | Solitone solutions complexifications of the Korteweg - de Vriz equation |
| title_fullStr | Solitone solutions complexifications of the Korteweg - de Vriz equation |
| title_full_unstemmed | Solitone solutions complexifications of the Korteweg - de Vriz equation |
| title_short | Solitone solutions complexifications of the Korteweg - de Vriz equation |
| title_sort | solitone solutions complexifications of the korteweg de vriz equation |
| topic | равнения в частных производных метод хироты точные решения нелинейных уравнений в частных производных соли-тоны автомодельное решение partial differential equations hirota method exact solutions of nonlinear partial differential equations solitons self-similar solution |
| url | https://scienceit.elpub.ru/jour/article/view/198 |
| work_keys_str_mv | AT tatyanavalentinovnaredkina solitonesolutionscomplexificationsofthekortewegdevrizequation |