As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber k in the direction the ridge, there is only one trapped wave (this was proved in Bonnet-Ben Dhia and Joly [Mathematical analysis of guided water waves, SIAM J. Appl. Math. 53 (1993) 1507–1550]. We construct asymptotics of these trapped waves and their frequencies as k→∞ by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov and Merzon [Asymptotics of eigenfunctions in shallow potential wells and related problems, Amer. Math. Soc. Trans. 208 (2) (2003) 235–284], in order to solve them.
展开▼
机译：众所周知，水下脊和淹没的水平圆柱体可以用作地表水波的波导。对于在山脊方向上的波数k较大的值，仅存在一个陷波（这在Bonnet-Ben Dhia和Joly中得到了证明[导水波的数学分析，SIAM J. Appl。Math。53（1993）1507）。 –1550]。通过将初始问题简化为一对边界积分方程，然后应用Zhevandrov和Merzon [浅势阱中的本征函数渐近]，我们将这些陷波及其频率的渐近性构造为k→∞。以及相关问题，Amer。Math。Soc。Trans。208（2）（2003）235-284]，以解决这些问题。
展开▼
