To the question of accounting in the equation of Korteweg – de Vriz of the dissipative term. Part 2 

Sergey O. Gladkov, Doctor of physical and mathematical sciences, professor, professor of the sub-department of applied software and mathematical methods, Moscow Aviation Institute (National Research University) (4 Volokolamskoye avenue, Moscow, Russia), E-mail: sglad51@mail.ru 

Background. When solving problems, the main character of which is the nonlinear equation of Korteweg de Vries (KdV), it is necessary to understand how calculations should be carried out taking into account the dissipative component. This point is quite relevant, and the main purpose of this report is precisely the analytical representation of the solution of the dissipative equation KdV. Materials and methods. The main method for solving the dissipative equation KdV, which is used in the work, is a formal transition to a new variable, which allows presenting the solution in the form of a soliton in a very compact form. Results and conclusions. The analysis given in the paper makes it possible to automatically take into account attenuation, which can be of a diverse nature depending on the real environment with which the soliton interacts. This result is the main conclusion of this communication. 

Korteweg de Vries equation, dissipation, nonlinear transformation 

Gladkov S.O. To the question of accounting in the equation of Korteweg – de Vriz of the dissipative term. Part 2. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2022;(4):42–46. (In Russ.). doi:10.21685/2072-3040-2022-4-4