ABSTRACT
Equations of the type https://www.w3.org/1998/Math/MathML"> D t u = D x 3 u + G ( u , D x u , D x 2 u ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/inline-math458.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> describe η – pseudospherical surfaces (see [11]). In paper [3] has been examined the equation https://www.w3.org/1998/Math/MathML"> D i u = a D x 3 u https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/inline-math459.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> which is called the Airy equation and is a linear version of the Korteweg - de Vries (KdV) equation. It arises in the description of the slow variation of a wave front in coordinates moving with the wave. It also describes the developments of long waves in various physical contexts, for example, plasma, water waves or nonlinear lattice.
