Abstract
Summary We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width � . Motivated by applications to surface wave propagation phenomena, we study the band-gap structure of the continuous spectrum. We show that for small apertures there exists a large number of gaps and also find asymptotic formulas for the position of the gaps as � → 0: the endpoints are determined within corrections of order � 3/2 . The width of the first bands is shown to be O(� ). Finally, we give a sufficient condition which guarantees that the spectral bands do not degenerate into eigenvalues of infinite multiplicity.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
