*Article* **A Deformed Wave Equation and Huygens' Principle**

### **Salem Ben Saïd \*, Sara al-Blooshi, Maryam al-Kaabi, Aisha al-Mehrzi and Fatima al-Saeedi**

Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box No. 15551, Al Ain, Abu Dhabi, UAE; 201502530@uaeu.ac.ae (S.a.-B.); 201506313@uaeu.ac.ae (M.a.-K.);

201601854@uaeu.ac.ae (A.a.-M.); 201735617@uaeu.ac.ae (F.a.-S.)

**\*** Correspondence: salem.bensaid@uaeu.ac.ae

Received: 1 October 2019; Accepted: 4 November 2019; Published: 19 December 2019

**Abstract:** We consider a deformed wave equation where the Laplacian operator has been replaced by a differential-difference operator.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 slp2, Rq.

**Keywords:** generalized Fourier transform; deformed wave equation; Huygens' principle; representation of slp2, Rq

**MSC:** 43A30; 22E70
