Classical Solutions for the Generalized Korteweg-de Vries Equation-Reference-Cited by-同舟云学术

Classical Solutions for the Generalized Korteweg-de Vries Equation

Published:2023-08-10 Issue:8 Volume:12 Page:777
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Georgiev Svetlin¹,Boukarou Aissa²^ORCID,Hajjej Zayd³,Zennir Khaled⁴^ORCID

Affiliation:

1. Department of Mathematics, Sorbonne University, 75005 Paris, France

2. Dynamic Systems Laboratory, Department of Mathematics, University of Science and Technology Houari Boumediene, Algiers 16111, Algeria

3. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

4. Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma, B.P. 401, Guelma 24000, Algeria

Abstract

The Korteweg-de Vries equation models the formation of solitary waves in the context of shallow water in a channel. In our system, f or p=2 and p=3 (Korteweg-de Vries equations (KdV)) and (modified Korteweg-de Vries (mKdV) respectively), these equations have many applications in Physics. (gKdV) is a Hamiltonian system. In this article we investigate the generalized Korteweg-de Vries (gKdV) equation. A new topological approach is applied to prove the existence of at least one classical solution. The arguments are based upon recent theoretical results.

Funder

King Saud University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/8/777/pdf

Reference9 articles.

1. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves;Korteweg;Lond. Edinb. Dublin Philos. Mag. J. Sci.,1895

2. The stability of solitary waves;Benjamin;Proc. Roy. Soc. Lond. A,1972

3. Eigenvalues, and instabilities of solita waves;Pego;Philos. Trans. Roy. Soc. Lond. A,1992

4. Asymptotic stabili, of solitary waves;Pego;Commun. Math. Phys.,1994

5. Smart, D.R. (1974). Fixed Point Theorems, Cambridge Vniversity Press.