EARLY DETECTION OF ROGUE WAVES USING COMPRESSIVE SAMPLING

Year 2019, Volume: 9 Issue: 2, 198 - 205, 01.06.2019

C. Bayındır

Abstract

We discuss the possible usage of the compressive sampling for the early detection of the rogue waves. One of the promising techniques for the early detection of the rogue waves is to measure the triangular Fourier spectra which begin to appear at the early stages of their development. For the early detection of the rogue waves it is possible to treat such a spectrum as a sparse signal since we would mainly be interested in the high amplitude triangular region located at the central wavenumber. Therefore compressive sampling can be a very ecient tool for the rogue wave early warning systems. By employing a numerical approach we show that triangular Fourier spectra can be sensed by compressive measurements at the early stages of the development of rogue waves such as those in the form of Peregrine and Akhmediev-Peregrine solitons. Our results may lead to development of the early warning and measurement systems which use the compressive sampling thus the memory requirements for those systems can be greatly reduced.

Keywords

Rogue waves, early detection, spectral analysis, compressive sensing.

References

• Kharif, C. and Pelinovsky, E., (2003), Physical mechanisms of the rogue wave phenomenon, European Journal of Mechanics B: Fluids., 22, pp. 603-634.
• Bayındır, C., (2016), Early detection of rogue waves by the wavelet transforms, Physics Letters A, 380, pp. 156-161.
• Akhmediev, N., Soto-Crespo, J. M., Ankiewicz, A. and Devine, N., (2011), Early detection of rogue waves in a chaotic wave field, Physics Letters A, 375, pp. 2999-3001.
• Zakharov, V. E., (1968), Stability of periodic waves of finite amplitude on the surface of a deep fluid, Soviet Physics JETP, 9, pp. 190-194.
• Akhmediev, N., Ankiewicz, A. and Soto-Crespo, J. M., (2009), Rogue waves and rational solutions of the nonlinear Schrdinger equation, Physical Review E, 80, 026601.
• Akhmediev, N., Soto-Crespo, J. M. and Ankiewicz, A., (2009), Extreme waves that appear from nowhere: On the nature of rogue waves, Physics Letters A, 373, pp. 2137-2145.
• Peregrine, D. H., (1983), Water waves, nonlinear Schrdinger equations and their solutions, Journal of Australian Mathematical Society: Series B, 25, pp. 16-43.
• Matveev, V. B. and Salle, M. A., (1991), Darboux Transformations and Solitons, Springer-Verlag, Berlin.
• Akhmediev, N., Ankiewicz, A., Soto-Crespo, J. M. and Dudley, J. M., (2011), Rogue wave early warning through spectral measurements?, Physics Letters A, 375, pp. 541-544.
• Trefethen, L. N., (2000), Spectral Methods in MATLAB, SIAM, Philadelphia.
• Bayındır, C., (2015), Compressive spectral method for the simulation of the water waves, arXiv Preprint, arXiv:1512.06286.
• Bayındır, C., (2009), Implementation of a computational model for random directional seas and underwater acoustics, MS Thesis, University of Delaware.
• Demiray, H. and Bayındır, C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Physics of Plasmas, 22, 092105.
• Karjadi, E. A., Badiey, M. and Kirby, J. T., (2010), Impact of surface gravity waves on highfrequency acoustic propagation in shallow water, The Journal of the Acoustical Society of America, 127, pp. 1787-1787.
• Karjadi, E. A., Badiey, M., Kirby, J. T. and Bayındır, C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE Journal of Oceanic Engineering, 37, pp. 112-121.
• Bayındır, C., (2015), Compressive split-step Fourier method, TWMS Journal of Applied and Engi- neering Mathematics, 5, pp. 298-306.
• Bayındır, C., (2015), Shapes and statistics of the rogue waves generated by chaotic ocean current, arXiv Preprint, arXiv:1512.03584.
• Bayındır, C., (2016), Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field, Physical Review E, 93, 032201.
• Bayındır, C., (2016), Rogue wave spectra of the Kundu-Eckhaus equation, Physical Review E, 93, 062215.
• Bayındır, C., (2016), Analytical and numerical aspects of the dissipative nonlinear Schrdinger equa- tion, TWMS Journal of Applied and Engineering Mathematics, 6, pp. 135-142.
• Bayındır, C., (2016), An extended Kundu-Eckhaus equation for modeling dynamics of rogue waves in a chaotic wave-current field, 12th International Congress on Advances in Civil Engineering, Istanbul. [22] Bayındır, C., (2017), Rogue wavefunctions due to noisy quantum tunneling potentials, TWMS Journal of Applied and Engineering Mathematics, 7, pp. 236-247.
• Bayındır, C., (2018), Compressive Spectral Renormalization Method, TWMS Journal of Applied and Engineering Mathematics, 8, pp. 425-437.
• Bayındır, C. and Ozaydin, F., (2018), Freezing optical rogue waves by Zeno dynamics, Optics Com- munications, 413, pp. 141-146.
• Candes, E. J., Romberg, J. and Tao, T., (2006), Robust uncertainty principles: exact signal recon- struction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52, pp. 489-509.
• Candes, E. J., (2006), Compressive sampling, Proceedings of the International Congress of Mathe- maticians, 3, pp. 1433-1452.