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In the Atmosphere and Oceanic Fluids: Scaling Transformations, Bilinear Forms, Bäcklund Transformations and Solitons for A Generalized Variable-Coefficient Korteweg-de Vries-Modified Korteweg-de Vries Equation.
- Source :
- China Ocean Engineering; Sep2021, Vol. 35 Issue 4, p518-530, 13p
- Publication Year :
- 2021
-
Abstract
- The atmosphere is an evolutionary agent essential to the shaping of a planet, while in oceanic science and daily life, liquids are commonly seen. In this paper, we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere, oceanic fluids and plasmas. With symbolic computation, beginning with a presumption, we work out certain scaling transformations, bilinear forms through the binary Bell polynomials and our scaling transformations, N solitons (with N being a positive integer) via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons. In addition, Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out. Respective dependences and constraints on the variable/constant coefficients are discussed, while those coefficients correspond to the quadratic-nonlinear, cubic-nonlinear, dispersive, dissipative and line-damping effects in the atmosphere, oceanic fluids and plasmas. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08905487
- Volume :
- 35
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- China Ocean Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 152371311
- Full Text :
- https://doi.org/10.1007/s13344-021-0047-7