Dispersion equation and eigenvalues for quantum wells using spectral parameter power series

Castillo-Pérez, Raúl; Kravchenko, Vladislav V.; Oviedo-Galdeano, H.; Rabinovich, Vladimir

doi:10.1063/1.3579991

Cited by 29 publications

(48 citation statements)

References 9 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

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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

Applicable Analysis

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“…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%

“…Moreover these methods need a large amount of the CPU times and the memory requirements for attaining reasonable results. [24,25] We proposed here for the analytical and numerical study of the problem (1)-(3) the SPPS method (see [26][27][28][29][30], and for the acoustic problems [1,2]). …”

Section: Introductionmentioning

confidence: 99%

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

Rabinovich

Juárez

2016

Applicable Analysis

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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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“…As was shown in a number of recent publications the SPPS representation provides an efficient and accurate method for solving initial value, boundary value and spectral problems (see [7], [8], [16], [21], [23], [22], [24], [25], [31], [32], [33], [35], [47]). In this paper we demonstrate this fact in application to equation (1.1).…”

Section: Introductionmentioning

confidence: 99%

Spectral parameter power series for Sturm-Liouville equations with a potential polynomially dependent on the spectral parameter and Zakharov-Shabat systems

Kravchenko

Torba

Velasco-García

2015

Journal of Mathematical Physics

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Abstract. A spectral parameter power series (SPPS) representation for solutions of Sturm-Liouville equations of the formis obtained. It allows one to write a general solution of the equation as a power series in terms of the spectral parameter λ. The coefficients of the series are given in terms of recursive integrals involving a particular solution of the equation (pu 0 ) +qu0 = 0. The convenient form of the solution of ( * ) provides an efficient numerical method for solving corresponding initial value, boundary value and spectral problems. A special case of the Sturm-Liouville equation ( * ) arises in relation with the Zakharov-Shabat system. We derive an SPPS representation for its general solution and consider other applications as the one-dimensional Dirac system and the equation describing a damped string. Several numerical examples illustrate the efficiency and the accuracy of the numerical method based on the SPPS representations which besides its natural advantages like the simplicity in implementation and accuracy is applicable to the problems admitting complex coefficients, spectral parameter dependent boundary conditions and complex spectrum.

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Dispersion equation and eigenvalues for quantum wells using spectral parameter power series

Cited by 29 publications

References 9 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

Spectral parameter power series for Sturm-Liouville equations with a potential polynomially dependent on the spectral parameter and Zakharov-Shabat systems

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