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Symmetry
Volume 15
Issue 2
10.3390/sym15020413
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Article

Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation

by
Wencheng Hu
1,2,
Jingli Ren
1 and
Yury Stepanyants
3,4,*
1
Henan Academy of Big Data, School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2
College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
3
School of Mathematics, Physics and Computing, University of Southern Queensland, 487–535 West St., Toowoomba, QLD 4350, Australia
4
Department of Applied Mathematics, Nizhny Novgorod State Technical University, n.a. R.E. Alekseev, 24 Minin St., Nizhny Novgorod 603950, Russia
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(2), 413; https://doi.org/10.3390/sym15020413
Submission received: 31 December 2022 / Revised: 15 January 2023 / Accepted: 28 January 2023 / Published: 3 February 2023
(This article belongs to the Special Issue Wave Processes in Fluids with Symmetric Density Stratification)
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Abstract

We consider approximate, exact, and numerical solutions to the cylindrical Korteweg–de Vries equation. We show that there are different types of solitary waves and obtain the dependence of their parameters on distance. Then, we study the interaction of solitary waves of different types.
Keywords: nonlinear wave; cylindrical Korteweg–De Vries equation; soliton; self-similar solitary wave nonlinear wave; cylindrical Korteweg–De Vries equation; soliton; self-similar solitary wave

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MDPI and ACS Style

Hu, W.; Ren, J.; Stepanyants, Y. Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation. Symmetry 2023, 15, 413. https://doi.org/10.3390/sym15020413

AMA Style

Hu W, Ren J, Stepanyants Y. Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation. Symmetry. 2023; 15(2):413. https://doi.org/10.3390/sym15020413

Chicago/Turabian Style

Hu, Wencheng, Jingli Ren, and Yury Stepanyants. 2023. "Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation" Symmetry 15, no. 2: 413. https://doi.org/10.3390/sym15020413

APA Style

Hu, W., Ren, J., & Stepanyants, Y. (2023). Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation. Symmetry, 15(2), 413. https://doi.org/10.3390/sym15020413

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