Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term
This paper investigates integrable properties of a generalized variable-coefficient Korteweg–de Vries (gvcKdV) equation incorporating dissipation, inhomogeneous media, and an external-force term. Based on Painlevé analysis, sufficient and necessary conditions for the equation’s Painlevé integrabilit...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/10/1642 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850126496636600320 |
|---|---|
| author | Gongxun Li Zhiyan Wang Ke Wang Nianqin Jiang Guangmei Wei |
| author_facet | Gongxun Li Zhiyan Wang Ke Wang Nianqin Jiang Guangmei Wei |
| author_sort | Gongxun Li |
| collection | DOAJ |
| description | This paper investigates integrable properties of a generalized variable-coefficient Korteweg–de Vries (gvcKdV) equation incorporating dissipation, inhomogeneous media, and an external-force term. Based on Painlevé analysis, sufficient and necessary conditions for the equation’s Painlevé integrability are obtained. Under specific integrability conditions, the Lax pair for this equation is successfully constructed using the extended Ablowitz–Kaup–Newell–Segur system (AKNS system). Furthermore, the Riccati-type Bäcklund transformation (R-BT), Wahlquist–Estabrook-type Bäcklund transformation (WE-BT), and the nonlinear superposition formula are derived. In utilizing these transformations and the formula, explicit one-soliton-like and two-soliton-like solutions are constructed from a seed solution. Moreover, the infinite conservation laws of the equation are systematically derived. Finally, the influence of variable coefficients and the external-force term on the propagation characteristics of a solitory wave is discussed, and soliton interaction is illustrated graphically. |
| format | Article |
| id | doaj-art-83cae6814e5d4324a606c6c06f82dbc5 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-83cae6814e5d4324a606c6c06f82dbc52025-08-20T02:33:55ZengMDPI AGMathematics2227-73902025-05-011310164210.3390/math13101642Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force TermGongxun Li0Zhiyan Wang1Ke Wang2Nianqin Jiang3Guangmei Wei4LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, ChinaLMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, ChinaLMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, ChinaSchool of Physics, Beihang University, Beijing 100191, ChinaLMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, ChinaThis paper investigates integrable properties of a generalized variable-coefficient Korteweg–de Vries (gvcKdV) equation incorporating dissipation, inhomogeneous media, and an external-force term. Based on Painlevé analysis, sufficient and necessary conditions for the equation’s Painlevé integrability are obtained. Under specific integrability conditions, the Lax pair for this equation is successfully constructed using the extended Ablowitz–Kaup–Newell–Segur system (AKNS system). Furthermore, the Riccati-type Bäcklund transformation (R-BT), Wahlquist–Estabrook-type Bäcklund transformation (WE-BT), and the nonlinear superposition formula are derived. In utilizing these transformations and the formula, explicit one-soliton-like and two-soliton-like solutions are constructed from a seed solution. Moreover, the infinite conservation laws of the equation are systematically derived. Finally, the influence of variable coefficients and the external-force term on the propagation characteristics of a solitory wave is discussed, and soliton interaction is illustrated graphically.https://www.mdpi.com/2227-7390/13/10/1642generalized variable-coefficient KdV equationPainlevé analysislax pairauto-Bäcklund transformationconservation law |
| spellingShingle | Gongxun Li Zhiyan Wang Ke Wang Nianqin Jiang Guangmei Wei Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term Mathematics generalized variable-coefficient KdV equation Painlevé analysis lax pair auto-Bäcklund transformation conservation law |
| title | Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term |
| title_full | Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term |
| title_fullStr | Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term |
| title_full_unstemmed | Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term |
| title_short | Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term |
| title_sort | analytic investigation of a generalized variable coefficient kdv equation with external force term |
| topic | generalized variable-coefficient KdV equation Painlevé analysis lax pair auto-Bäcklund transformation conservation law |
| url | https://www.mdpi.com/2227-7390/13/10/1642 |
| work_keys_str_mv | AT gongxunli analyticinvestigationofageneralizedvariablecoefficientkdvequationwithexternalforceterm AT zhiyanwang analyticinvestigationofageneralizedvariablecoefficientkdvequationwithexternalforceterm AT kewang analyticinvestigationofageneralizedvariablecoefficientkdvequationwithexternalforceterm AT nianqinjiang analyticinvestigationofageneralizedvariablecoefficientkdvequationwithexternalforceterm AT guangmeiwei analyticinvestigationofageneralizedvariablecoefficientkdvequationwithexternalforceterm |