scholarly journals Two Parameters Deformations of Ninth Peregrine Breather Solution of the NLS Equation and Multi-Rogue Waves

2013 ◽  
Vol 2013 ◽  
pp. 1-105 ◽  
Author(s):  
Pierre Gaillard
Keyword(s):  
Efficient Method ◽  
Rogue Waves ◽  
Nls Equation ◽  
Analytical Expression ◽  
Breather Solution ◽  
Method Of Determination ◽  
Two Parameters ◽  
Peregrine Breather

This paper is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and their deformations. Here we construct Peregrine breathers of order and multi-rogue waves associated by deformation of parameters. The analytical expression corresponding to Peregrine breather is completely given.

Current Effects on the Generation and Evolution of the Peregrine Breather-Type Rogue Wave

2015 ◽  
Author(s):  
Wenyue Lu ◽  
Jianmin Yang ◽  
Longbin Tao ◽  
Haining Lu ◽  
Xinliang Tian ◽  
...  
Keyword(s):  
Rogue Wave ◽  
Evolutionary Process ◽  
Rogue Waves ◽  
Nls Equation ◽  
Sea State ◽  
Steady Current ◽  
Wave Heights ◽  
Current Interaction ◽  
Physical Mechanics ◽  
Peregrine Breather

Rogue wave is a kind of surface gravity waves with much larger wave heights than expected in normal sea state. Since this extreme sea event always occurred in the areas with strong currents, the wave-current interaction was considered to be one of the physical mechanics of the formation of the rogue wave. Some breather type solutions of the NLS equation have been considered as prototypes of rogue waves in ocean which usually appears from smooth initial condition only with a certain disturbance. In this paper, we have numerically studied evolutionary process of the Peregrine breather rogue wave based on the current modified fourth order nonlinear Schrödinger equation (the CmNLS equation). During the generation and evolution of the Peregrine breather rogue wave, the effects of the steady current was investigated by comparing with the results without current. The differences of the focusing position/time were observed due to the current influence.

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

2015 ◽  
Vol 26 (02) ◽  
pp. 1550016 ◽  
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.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

Development of a method for multielemental determination in water by EDXRF with radioisotopic source of 238Pu.

2019 ◽  
Vol 7 (2A) ◽  
Author(s):  
Camilo Fuentes Serrano ◽  
Juan Reinaldo Estevez Alvares ◽  
Alfredo Montero Alvarez ◽  
Ivan Pupo Gonzales ◽  
Zahily Herrero Fernandez ◽  
...  
Keyword(s):  
Thin Layer ◽  
Expanded Uncertainty ◽  
Considerable Decrease ◽  
X Ray ◽  
Precipitation Efficiency ◽  
Method Of Determination ◽  
Sensitivity Curves ◽  
Order Of Magnitude ◽  
Metrological Parameters

A method for determination of Cr, Fe, Co, Ni, Cu, Zn, Hg and Pb in waters by Energy Dispersive X Ray Fluorescence (EDXRF) was implemented, using a radioisotopic source of 238Pu. For previous concentration was employed a procedure including a coprecipitation step with ammonium pyrrolidinedithiocarbamate (APDC) as quelant agent, the separation of the phases by filtration, the measurement of filter by EDXRF and quantification by a thin layer absolute method. Sensitivity curves for K and L lines were obtained respectively. The sensitivity for most elements was greater by an order of magnitude in the case of measurement with a source of 238Pu instead of 109Cd, which means a considerable decrease in measurement times. The influence of the concentration in the precipitation efficiency was evaluated for each element. In all cases the recoveries are close to 100%, for this reason it can be affirmed that the method of determination of the studied elements is quantitative. Metrological parameters of the method such as trueness, precision, detection limit and uncertainty were calculated. A procedure to calculate the uncertainty of the method was elaborated; the most significant source of uncertainty for the thin layer EDXRF method is associated with the determination of instrumental sensitivities. The error associated with the determination, expressed as expanded uncertainty (in %), varied from 15.4% for low element concentrations (2.5-5 μg/L) to 5.4% for the higher concentration range (20-25 μg/L).

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