TY - JOUR

T1 - Spectral gaps for the linear surface wave model in periodic channels

AU - Bakharev, F.L.

AU - Ruotsalainen, K.

AU - Taskinen, J.

PY - 2014

Y1 - 2014

N2 - We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width ɛ. 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 ɛ → 0: the endpoints are determined within corrections of order ɛ^{3/2}. The width of the first bands is shown to be O(ɛ). Finally, we give a sufficient condition which guarantees that the spectral bands do not degenerate into eigenvalues of infinite multiplicity.

AB - We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width ɛ. 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 ɛ → 0: the endpoints are determined within corrections of order ɛ^{3/2}. The width of the first bands is shown to be O(ɛ). Finally, we give a sufficient condition which guarantees that the spectral bands do not degenerate into eigenvalues of infinite multiplicity.

KW - band-gap sructure

U2 - 10.1093/qjmam/hbu009

DO - 10.1093/qjmam/hbu009

M3 - Article

VL - 67

SP - 343

EP - 362

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 3

ER -