Communications in Mathematical Analysis

A Note on Embedded Trapped Modes for a Two-layer Fluid over a Rectangular Barrier

M. I. Romero Rodriguez and P. Zhevandrov

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We prove that the system of equations describing waves in a two-layer fluid over a rectangular barrier of small height possesses embedded trapped modes (eigenvalues submerged in the continuous spectrum) for certain values of the width of the barrier and that these eigenvalues are analytic in the small parameter characterizing the height of the barrier. We do this by means of purely elementary considerations constructing explicit solutions and thus confirm the results of [7] obtained for general perturbations of the depth of the fluid in the particular case of a rectangular barrier.

Article information

Commun. Math. Anal., Volume 17, Number 2 (2014), 338-343.

First available in Project Euclid: 18 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76B70: Stratification effects in inviscid fluids 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.)

embedded eigenvalues two-layer fluid


Romero Rodriguez, M. I.; Zhevandrov, P. A Note on Embedded Trapped Modes for a Two-layer Fluid over a Rectangular Barrier. Commun. Math. Anal. 17 (2014), no. 2, 338--343.

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