Impact of surface gravity waves on high-frequency acoustic propagation in shallow water.

Karjadi, Entin A.; Badiey, Mohsen; Kirby, James T.

doi:10.1121/1.3383959

Cited by 18 publications

(15 citation statements)

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“…Some of these techniques are the shooting, self-consistency and relaxation techniques [21][22][23][24][25]. One of the most commonly used methods for this purpose is the Petviashvili's method, in which the governing nonlinear equation is transformed into Fourier space similar to the other Fourier spectral methods using FFT routines [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Then, a convergence factor is used in accordance with the degree of the nonlinear term [21,22].…”

Section: Spectral Renormalization Methods For Finding the Self-locali...mentioning

confidence: 99%

Self-Localized Solutions of the Nonlinear Quantum Harmonic Oscillator

Bayindir

2019

Preprint

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We analyze the existences, properties and stabilities of the self-localized solutions of the nonlinear quantum harmonic oscillator (NQHO) using spectral renormalization method (SRM). We show that self-localized single, dual and triple soliton solutions of the NQHO do exists, however only single and dual soliton solutions satisfy the necessary Vakhitov and Kolokolov slope condition, therefore triple soliton solution is found to be unstable, at least for the parameter ranges considered. Additionally, we investigate the stability characteristics of the single and dual soliton solutions using a split-step Fourier scheme. We show that single and dual soliton solutions are pulsating during time stepping. We discuss our findings and comment on our results.

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Section: Spectral Renormalization Methods For Finding the Self-locali...mentioning

confidence: 99%

Self-Localized Solutions of the Nonlinear Quantum Harmonic Oscillator

Bayindir

2019

Preprint

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“…The high order spectral method summarized in this section is first presented in 4 ; which models the nonlinear ocean surface waves on the surface of an ideal fluid. An implementation of this model both in 1D and 2D can be seen in 1 2 3 5 .…”

Section: Methodsmentioning

confidence: 99%

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

Bayındır

2016

Sci Rep

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In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions.

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“…In SSFM schemes, the spatial derivatives are evaluated using spectral techniques. Some of the applications of the spectral techniques can be seen in [7,19,20] and more detailed discussions can be seen in [23]. In spectral techniques the spatial derivatives are calculated by making use of the orthogonal transforms.…”

Section: Chaotic Wave Fieldsmentioning

confidence: 99%

Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field

Bayındır

2016

Phys. Rev. E

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In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.

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Impact of surface gravity waves on high-frequency acoustic propagation in shallow water.

Cited by 18 publications

References 0 publications

Self-Localized Solutions of the Nonlinear Quantum Harmonic Oscillator

Self-Localized Solutions of the Nonlinear Quantum Harmonic Oscillator

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field

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