Classical Solutions for the Generalized Korteweg-de Vries Equation

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...

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Bibliographic Details
Published inAxioms Vol. 12; no. 8; p. 777
Main Authors Georgiev, Svetlin, Boukarou, Aissa, Hajjej, Zayd, Zennir, Khaled
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2023
Subjects
Banach spaces
classical solution
Differential equations, Partial
existence
gKdV equation
Hamiltonian functions
Hypotheses
Korteweg-Devries equation
Mathematical research
Shallow water
Solitary waves
Theorems
France
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12080777