A Deformed Wave Equation and Huygens’ Principle

A Deformed Wave Equation and Huygens’ Principle

We consider a deformed wave equation where the Laplacian operator has been replaced by a differential-difference operator. We prove that this equation does not satisfy Huygens’ principle. Our approach is based on the representation theory of the Lie algebra s l ( 2 , R ) .

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Veröffentlicht in:Mathematics (Basel) 2020-01, Vol.8 (1), p.10
Hauptverfasser: Ben Saïd, Salem, al-Blooshi, Sara, al-Kaabi, Maryam, al-Mehrzi, Aisha, al-Saeedi, Fatima
Format: Artikel
Sprache:eng
Schlagworte:
Cauchy problems
Deformation
Differential equations
Finite differences
Fourier transforms
Lie groups
Mathematical functions
Mathematics
Operators (mathematics)
Wave equations
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Zusammenfassung:We consider a deformed wave equation where the Laplacian operator has been replaced by a differential-difference operator. We prove that this equation does not satisfy Huygens’ principle. Our approach is based on the representation theory of the Lie algebra s l ( 2 , R ) .
ISSN:2227-7390
2227-7390
DOI:10.3390/math8010010