This article is cited in 2 papers

Mathematics

On the issue of accounting dissipative term in the Korteweg - de Vriz equation

S. O. Gladkov

Moscow Aviation Institute (National Research University) (MAI), Moscow, Russia

Abstract: Background. Any partial notch equation, and even more so a nonlinear one, including the Korteweg - de Vries equation, requires certain methodological approaches in order to find its solutions. Since, in solving specific physical problems, it is necessary to take into account the presence of a real environment, the actual point here is to take into account the dissipative term in the KdV equation, and which should be written in general form for any issue, which is the main purpose of this message. Materials and methods. When solving the KdV equation, we get a solution in the form of a soliton, which, as is known, has the form of an inverse function on the square of the hyperbolic cosine. Therefore, when solving a problem taking into account dissipation, we need to take into account its general solutions and introduce a temporary dependence into it using the method of the inverse problem, which is done in this work. Results and conclusions. The KdV equation obtained in general form, taking into account attenuation, can be used, for example, when solving problems of studying magnetoplasmic waves. But the main result of the research is the possibility of studying any dissipative phenomena in which the soliton takes part.

Keywords: Korteweg - de Vries equation, soliton, dissipative terms.

UDC: 533.9.01

DOI: 10.21685/2072-3040-2022-1-3

Bibliographic databases:

•