Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework
Hirota’s direct method is one significant way to obtain solutions of soliton equations, but it is rarely studied under the time scale framework. In this paper, the generalized KdV equation on time-space scale is deduced from one newly constructed Lax equation and zero curvature equation by using the...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/4407753 |
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| author | Yuan Kong Xing-Chen Liu Huan-He Dong Ming-Shuo Liu Chun-Ming Wei Xiao-Qian Huang Yong Fang |
| author_facet | Yuan Kong Xing-Chen Liu Huan-He Dong Ming-Shuo Liu Chun-Ming Wei Xiao-Qian Huang Yong Fang |
| author_sort | Yuan Kong |
| collection | DOAJ |
| description | Hirota’s direct method is one significant way to obtain solutions of soliton equations, but it is rarely studied under the time scale framework. In this paper, the generalized KdV equation on time-space scale is deduced from one newly constructed Lax equation and zero curvature equation by using the AKNS method, which can be reduced to the classical and discrete KdV equation by considering different time scales. What is more, it is the first time that the single-soliton solution of the KdV equation under the time scale framework is obtained by using the idea of Hirota’s direct method. |
| format | Article |
| id | doaj-art-90d974eb361f4bb7be89dbd31013ef72 |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-90d974eb361f4bb7be89dbd31013ef722025-02-03T00:59:36ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/4407753Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale FrameworkYuan Kong0Xing-Chen Liu1Huan-He Dong2Ming-Shuo Liu3Chun-Ming Wei4Xiao-Qian Huang5Yong Fang6College of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceHirota’s direct method is one significant way to obtain solutions of soliton equations, but it is rarely studied under the time scale framework. In this paper, the generalized KdV equation on time-space scale is deduced from one newly constructed Lax equation and zero curvature equation by using the AKNS method, which can be reduced to the classical and discrete KdV equation by considering different time scales. What is more, it is the first time that the single-soliton solution of the KdV equation under the time scale framework is obtained by using the idea of Hirota’s direct method.http://dx.doi.org/10.1155/2022/4407753 |
| spellingShingle | Yuan Kong Xing-Chen Liu Huan-He Dong Ming-Shuo Liu Chun-Ming Wei Xiao-Qian Huang Yong Fang Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework Advances in Mathematical Physics |
| title | Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework |
| title_full | Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework |
| title_fullStr | Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework |
| title_full_unstemmed | Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework |
| title_short | Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework |
| title_sort | single soliton solution of kdv equation via hirota s direct method under the time scale framework |
| url | http://dx.doi.org/10.1155/2022/4407753 |
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