Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation

Abstract. We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto-acoustic waves in plasma (Zhdanov, 1984) etc. In addition, there are plenty of equations of physical importance, having their origin in fiber optics, hydrodynamics, plasma physics and many other areas, which are gauge equivalent to the NLS equation or to the KP-I equation. Therefore our results can be easily extended to a large number of systems of physical interest to be discussed in separate publications.

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A variable coefficient nonlinear Schrödinger equation: localized waves on the plane wave background and their dynamics

Modern Physics Letters B ◽

10.1142/s0217984919501215 ◽

2019 ◽

Vol 33 (10) ◽

pp. 1850121 ◽

Cited By ~ 1

Author(s):

Xiu-Bin Wang ◽

Bo Han

Keyword(s):

Variable Coefficient ◽

Rogue Wave ◽

Rogue Waves ◽

Rational Solutions ◽

Nls Equation ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Plane Wave Background ◽

Localized Waves ◽

Similarity Reductions

In this work, a variable coefficient nonlinear Schrödinger (vc-NLS) equation is under investigation, which can describe the amplification or absorption of pulses propagating in an optical fiber with distributed dispersion and nonlinearity. By means of similarity reductions, a similar transformation helps us to relate certain class of solutions of the standard NLS equation to the solutions of integrable vc-NLS equation. Furthermore, we analytically consider nonautonomous breather wave, rogue wave solutions and their interactions in the vc-NLS equation, which possess complicated wave propagation in time and differ from the usual breather waves and rogue waves. Finally, the main characteristics of the rational solutions are graphically discussed. The parameters in the solutions can be used to control the shape, amplitude and scale of the rogue waves.

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Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2014.0318 ◽

2014 ◽

Vol 470 (2171) ◽

pp. 20140318 ◽

Cited By ~ 39

Author(s):

Jingsong He ◽

Lijuan Guo ◽

Yongshuai Zhang ◽

Amin Chabchoub

Keyword(s):

Deep Water ◽

Rogue Waves ◽

Nls Equation ◽

Third Order ◽

Weakly Nonlinear ◽

Wave Flume ◽

Symmetric Pattern ◽

System A ◽

Special Case ◽

Good Agreement

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

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Numerical Simulation on Nonlinear Evolution of Rogue Waves on Currents Based on the NLS Equation

Volume 2: Structures, Safety and Reliability ◽

10.1115/omae2011-50079 ◽

2011 ◽

Cited By ~ 3

Author(s):

Hanhong Hu ◽

Ning Ma

Keyword(s):

Numerical Simulation ◽

Deep Water ◽

Water Waves ◽

Rogue Waves ◽

Domain Model ◽

Energy Concentration ◽

Current Field ◽

Nls Equation ◽

Steady Current ◽

Deep Water Wave

In this paper, nonlinear instability and evolution of deep-water rogue waves on following and opposing currents were described by numerical simulation for laboratory investigation. The generation of rogue waves in a numerical tank by means of wave focusing technique had been studied. Here a spatial domain model of current modified nonlinear Schro¨dinger (NLSC) equations in one horizontal dimension (1D) was established for describing the deep-water wave trains in a prescribed stationary current field. The transient water waves (TWW) was adopted as the initial condition of the NLSC equation. The steady current was added to see the effect of wave-current interaction on the energy concentration of gravity waves. The influence of current as well as other terms in the NLSC equations on wave height, inclination, particle velocity and acceleration are shown. Meanwhile, the focusing time/position of TWW influenced by the current field is investigated, which is of course a very important factor in experimental research when we generate rogue waves in the laboratory.

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Families of quasi-rational solutions of the NLS equation and multi-rogue waves

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/44/43/435204 ◽

2011 ◽

Vol 44 (43) ◽

pp. 435204 ◽

Cited By ~ 87

Author(s):

Pierre Gaillard

Keyword(s):

Rogue Waves ◽

Rational Solutions ◽

Nls Equation

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Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

Modern Physics Letters B ◽

10.1142/s0217984917502980 ◽

2017 ◽

Vol 31 (32) ◽

pp. 1750298 ◽

Cited By ~ 9

Author(s):

Meidan Chen ◽

Biao Li

Keyword(s):

Rogue Wave ◽

Soliton Solutions ◽

Rogue Waves ◽

Rational Solutions ◽

Nls Equation ◽

Bilinear Method ◽

Nonlinear Schrödinger ◽

Long Wave ◽

Hybrid Solutions ◽

Wave Limit

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.

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18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation

International Journal of Modern Physics C ◽

10.1142/s0129183115500163 ◽

2015 ◽

Vol 26 (02) ◽

pp. 1550016 ◽

Cited By ~ 4

Author(s):

Pierre Gaillard ◽

Mickaël Gastineau

Keyword(s):

Rogue Waves ◽

Rational Solutions ◽

Nls Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Different Types ◽

Peregrine Breather

We present here new solutions of the focusing one-dimensional nonlinear Schrödinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.

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Nonplanar dust acoustic waves in a four-component dusty plasma with double spectral distributed electrons: modulational instability and rogue waves

Waves in Random and Complex Media ◽

10.1080/17455030.2021.1951886 ◽

2021 ◽

pp. 1-20

Author(s):

S. K. El-Labany ◽

W. F. El-Taibany ◽

A. A. El-Tantawy ◽

N. A. Zedan

Keyword(s):

Dusty Plasma ◽

Acoustic Waves ◽

Modulational Instability ◽

Rogue Waves ◽

Dust Acoustic Waves ◽

Dust Acoustic

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Recent Advances in Phase-Sensitive Optical Time Domain Reflectometry (Ф-OTDR)

Photonic Sensors ◽

10.1007/s13320-021-0619-4 ◽

2021 ◽

Vol 11 (1) ◽

pp. 1-30

Author(s):

Yunjiang Rao ◽

Zinan Wang ◽

Huijuan Wu ◽

Zengling Ran ◽

Bing Han

Keyword(s):

Fiber Optics ◽

Time Domain ◽

Acoustic Waves ◽

Rapid Development ◽

Development Stage ◽

Time Domain Reflectometry ◽

Rayleigh Backscattering ◽

Optical Time Domain Reflectometry ◽

Phase Sensitive ◽

Optical Time

AbstractPhase-sensitive optical time domain reflectometry (Ф-OTDR) is an effective way to detect vibrations and acoustic waves with high sensitivity, by interrogating coherent Rayleigh backscattering light in sensing fiber. In particular, fiber-optic distributed acoustic sensing (DAS) based on the Ф-OTDR with phase demodulation has been extensively studied and widely used in intrusion detection, borehole seismic acquisition, structure health monitoring, etc., in recent years, with superior advantages such as long sensing range, fast response speed, wide sensing bandwidth, low operation cost and long service lifetime. Significant advances in research and development (R&D) of Ф-OTDR have been made since 2014. In this review, we present a historical review of Ф-OTDR and then summarize the recent progress of Ф-OTDR in the Fiber Optics Research Center (FORC) at University of Electronic Science and Technology of China (UESTC), which is the first group to carry out R&D of Ф-OTDR and invent ultra-sensitive DAS (uDAS) seismometer in China which is elected as one of the ten most significant technology advances of PetroChina in 2019. It can be seen that the Ф-OTDR/DAS technology is currently under its rapid development stage and would reach its climax in the next 5 years.

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