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Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation
- Source :
- Mathematics, Vol 10, Iss 414, p 414 (2022), Mathematics; Volume 10; Issue 3; Pages: 414
- Publication Year :
- 2022
- Publisher :
- MDPI AG, 2022.
-
Abstract
- In this paper, we study a generalized scale-invariant analogue of the well-known Korteweg–de Vries (KdV) equation. This generalized equation can be thought of as a bridge between the KdV equation and the SIdV equation that was discovered recently, and shares the same one-soliton solution as the KdV equation. By employing the auxiliary equation method, we are able to obtain a wide variety of traveling wave solutions, both bounded and singular, which are kink and bell types, periodic waves, exponential waves, and peaked (peakon) waves. As far as we know, these solutions are new and their explicit closed-form expressions have not been reported elsewhere in the literature.
- Subjects :
- auxiliary equation method
General Mathematics
generalized SIdV equation
exact traveling waves
solitary waves—kink and bell types
periodic waves
peakon
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Computer Science (miscellaneous)
QA1-939
Engineering (miscellaneous)
Nonlinear Sciences::Pattern Formation and Solitons
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 414
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....f4d1ceba89f25b72a3e6262249010f83