ABOUT ONE CLASS OF DIFFERENTIAL EQUATIONS WITH SOLUTIONS IN THE FORM OF SOLITATED WAVES
https://doi.org/10.26583/vestnik.2023.304
Abstract
A special class of nonlinear differential equations with solutions in the form of solitary waves is considered. The main feature of these differential equations is that they have a solution in the complex plane with an arbitrary pole order. It is shown that using a modification of the method of simple equations allows one to find exact solutions in the form of solitary waves. The presented method is used to obtain stationary solitary waves to describe processes in a liquid with gas bubbles. Also, this method is used to find stationary solitary waves of bacterial concentration when taking phototaxis into account.
About the Authors
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
N. V. Ermolaeva
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute); Volgodonsk Engineering Technical Institute the branch of National Research Nuclear University MEPhI
Russian Federation
Russian Federation
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Review
For citations:
Kudryashov N.A., Ermolaeva N.V. ABOUT ONE CLASS OF DIFFERENTIAL EQUATIONS WITH SOLUTIONS IN THE FORM OF SOLITATED WAVES. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(6):321-325. (In Russ.) https://doi.org/10.26583/vestnik.2023.304
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