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.

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]