Spectral parameter power series analysis of isotropic planarly layered waveguides

Barrera-Figueroa, V.; Kravchenko, Vladislav V.; Rabinovich, Vladimir

doi:10.1080/00036811.2013.794940

Cited by 16 publications

(28 citation statements)

References 28 publications

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“…For the details of an iterative construction of a solution u 0 of the homogeneous Equation (19) and particular solutions u 1 , u 2 , and numerical methods of its calculation see [25], and also [28,29].…”

Section: Methods Of the Sppsmentioning

confidence: 99%

“…Moreover these methods need a large amount of C PU times and memory requirements for attaining reasonable results. [22,23] We proposed here for the analytical and numerical study of the problem (1)-(3) the SPPS method (see [24][25][26][27][28][29]). Applying the SPPS method, we obtain an explicit analytical form for a dispersion equation D(ω, μ) = 0, defining the wave numbers μ j (ω), j = 1, .…”

Section: Introductionmentioning

confidence: 99%

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Effective methods of estimates of acoustic fields in the ocean generated by moving sources

Rabinovich

Juárez

2015

Applicable Analysis

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We consider underwater acoustic fields generated by non-uniformly moving modulated sources. We introduce a large parameter λ > 0 which characterizing simultaneously a slowness of variations of source amplitudes, and their horizontal velocities, and a large distances between sources and receivers with respect to the characteristic length of the acoustic wave. We present the asymptotic formulas for the acoustic fields as a sum of propagating modes. Applying the spectral parameter power series method (SPPS method), we obtain an analytic form of the dispersion equation and the propagating modes. We show that the SPPS method is an effective tool for the numerical implementation of the underwater acoustic fields generated by non uniformly moving sources.

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Section: Methods Of the Sppsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effective methods of estimates of acoustic fields in the ocean generated by moving sources

Rabinovich

Juárez

2015

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“…(For the details of an iterative construction of a solution u 0 of the homogeneous Equation (36) and particular solutions u 1 , u 2 of Equation (39) and numerical methods of its calculation see [26,29,30]. )…”

Section: Numerical Calculation Of the Modes Contributionmentioning

confidence: 99%

“…For this aim we use the method of SPPS (see [26][27][28][29][30]) and [1,2] for the acoustics problems).…”

Section: Numerical Calculation Of the Modes Contributionmentioning

confidence: 99%

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Numerical estimates of acoustic fields in the ocean generated by moving airborne sources

Rabinovich

Juárez

2016

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We investigate the underwater acoustic field in the stratified ocean generated by moving in the air sources. We obtain asymptotic formulas expressed in terms of the retarded time and the Doppler-shifted frequency. The spectral parameter power series method is implemented to find the wave numbers of the propagating modes, their group velocity and an analytic form of the acoustic field in the ocean. Some numerical results are presented. ARTICLE HISTORY

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Asymptotics of the far field generated by a modulated point source in a planarly layered electromagnetic waveguide

Barrera-Figueroa

Rabinovich²

2014

Math Methods in App Sciences

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Communicated by S. TorbaIn the present work, we analyze the electromagnetic field generated by a modulated point source in a planarly layered waveguide, in the far field region. On the basis of the two-dimensional stationary phase method, we obtain expressions for the asymptotics of the field at large distance from the source and a large value of the time. The analysis relies on the eigenfunctions and eigenvalues of an auxiliary one-dimensional spectral problem, which is intimately linked to the Helmholtz equation for inhomogeneous media. In addition, from the spectral parameter power series method [Math. Meth. Appl. Sci. 2010; 33(4): 459-468], we obtain an explicit representation for the dispersion relation of the waveguide, which leads us to the allowed propagation constants and the group velocities for the guided modes. Several examples show the spectral parameter power series approach of the present analysis.

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Spectral parameter power series analysis of isotropic planarly layered waveguides

Cited by 16 publications

References 28 publications

Effective methods of estimates of acoustic fields in the ocean generated by moving sources

Effective methods of estimates of acoustic fields in the ocean generated by moving sources

Numerical estimates of acoustic fields in the ocean generated by moving airborne sources

Asymptotics of the far field generated by a modulated point source in a planarly layered electromagnetic waveguide

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