A Deformed Wave Equation and Huygens’ Principle

Salem Ben Saïd, Sara al-Blooshi, Maryam al-Kaabi, Aisha al-Mehrzi and Fatima al-Saeedi
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Salem Ben Saïd: Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box No. 15551, Al Ain, Abu Dhabi, UAE
Sara al-Blooshi: Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box No. 15551, Al Ain, Abu Dhabi, UAE
Maryam al-Kaabi: Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box No. 15551, Al Ain, Abu Dhabi, UAE
Aisha al-Mehrzi: Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box No. 15551, Al Ain, Abu Dhabi, UAE
Fatima al-Saeedi: Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box No. 15551, Al Ain, Abu Dhabi, UAE

Mathematics, 2019, vol. 8, issue 1, 1-11

Abstract: We consider a deformed wave equation where the Laplacian operator has been replaced by a differential-difference operator.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 ) .

Keywords: generalized Fourier transform; deformed wave equation; Huygens’ principle; representation of s l ( 2 , R ) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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