title: A Hamiltonian method for finding broadband modal eigenvalues.
abstract: For shallow water waveguides over a layered elastic bottom, modal eigenvalues can be determined by searching the locations in the complex plane of the horizontal wave number at which the complex phase function is a multiple of π [C. T. Tindle and N. R. Chapman, J. Acoust. Soc. Am. 96, 1777-1782 (1994)]. In this paper, a Hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real. The Hamiltonian method can also be extended to compute the broadband modal eigenvalues or the modal dispersion curves in the Pekeris waveguide with fluid/elastic bottoms. For each proper or leaky normal mode, a different Hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigenvalue in a reference frequency as the initial value. In contrast to the usual methods, the dispersion curve for each mode is determined individually. The Hamiltonian method shows good performance by comparing with KRAKEN.
authors.affiliation: College of Information Science and Technology, Ocean University of China, 238 Songling Road, Qingdao, 266100, People's Republic of China. coolicejiao@hotmail.com
authors.forename: Haozhong
authors.initials: H
authors.lastname: Wang
authors.forename: Ning
authors.initials: N
authors.lastname: Wang
authors.forename: Dazhi
authors.initials: D
authors.lastname: Gao