REMARKS ON SOLITARY WAVES IN EQUATIONS WITH NONLOCAL CUBIC TERMS
Journal article, Peer reviewed
Accepted version
Permanent lenke
https://hdl.handle.net/11250/3135595Utgivelsesdato
2024Metadata
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- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38672]
Sammendrag
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form ∂tu +∂x(Λsu+uΛru2) = 0, where Λs,Λr are Bessel-type Fourier multipliers. The linear operator may be of low fractional order, s > 0, while the operator on the nonlinear part is assumed to act slightly smoother, r < s − 1. The problem is related to the mathematical theory of water waves; we build upon previous works on similar equations, extending them to allow for a nonlocal nonlinearity. Mathematical tools include constrained minimization, Lion’s concentration–compactness principle, spectral estimates, and product estimates in fractional Sobolev spaces.