Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation-Reference-Cited by-同舟云学术

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

Published:2023-02-03 Issue:2 Volume:15 Page:413
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Hu Wencheng¹²^ORCID,Ren Jingli¹^ORCID,Stepanyants Yury³⁴^ORCID

Affiliation:

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

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.

Funder

China Scholarship Council

National Natural Science Foundation of China

President Council of the Russian Federation for the State support of Leading Scientific Schools of the Russian Federation

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/2/413/pdf

Reference41 articles.

1. On the asymptotic of an axisymmetric divergent wave in a heavy fluid;Iordansky;Dokl. Akad. Sci. USSR,1959

2. Initial conditions for the cylindrical Korteweg–de Vries equation;Grimshaw;Stud. Appl. Math.,2019

3. On the nonlinear internal wave theory in fluid of finite depth;Lipovskii;Izv. Akad. Nauk SSSR Fiz. Atm. Okeana,1985

4. Viecelli, Cylindrical solitons;Maxon;Phys. Fluids,1974

5. An axisymmetric Boussinesq wave;Miles;J. Fluid Mech.,1978

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