Abstract
As is well known, submerged horizontal cylinders can serve as waveguides for
surface water waves. For large values of the wavenumber
As is well known, submerged horizontal cylinders can serve as waveguides for
surface water waves. For large values of the wavenumber
F. Ursell, “Trapping modes in the theory of surface waves,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 47, pp. 347–358, 1951.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA.-S. Bonnet-Ben Dhia and P. Joly, “Mathematical analysis of guided water waves,” SIAM Journal on Applied Mathematics, vol. 53, no. 6, pp. 1507–1550, 1993.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetN. Kuznetsov, V. Maz'ya, and B. Vainberg, Linear Water Waves, Cambridge University Press, Cambridge, UK, 2002.
View at: Zentralblatt MATH | MathSciNetA. M. Marín, R. D. Ortíz, and P. Zhevandrov, “High-frequency asymptotics of waves trapped by underwater ridges and submerged cylinders,” Journal of Computational and Applied Mathematics, vol. 204, no. 2, pp. 356–362, 2007.
View at: Publisher Site | Google ScholarP. Zhevandrov and A. Merzon, “Asymptotics of eigenfunctions in shallow potential wells and related problems,” in Asymptotic Methods for Wave and Quantum Problems, vol. 208 of Amer. Math. Soc. Transl. Ser. 2, pp. 235–284, American Mathematical Society, Providence, RI, USA, 2003.
View at: Google Scholar | MathSciNetL. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory. Course of Theoretical Physics, Vol. 3, Addison-Wesley Series in Advanced Physics, Pergamon, London, UK, 1958.
View at: Zentralblatt MATH | MathSciNetB. Simon, “The bound state of weakly coupled Schrödinger operators in one and two dimensions,” Annals of Physics, vol. 97, no. 2, pp. 279–288, 1976.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. R. Gadyl'shin, “On local perturbations of the Schrödinger operator on the axis,” Theoretical and Mathematical Physics, vol. 132, no. 1, pp. 976–982, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. S. Kuznetsov, “A spectrum perturbation problem and its application to waves above an underwater ridge,” Siberian Mathematical Journal, vol. 42, no. 4, pp. 668–684, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1970.