Search results for "Akhmediev's solutions."
showing 5 items of 5 documents
Deformations of the seventh order Peregrine breather solutions of the NLS equation with twelve parameters.
2013
We study the solutions of the one dimensional focusing NLS equation. Here we construct new deformations of the Peregrine breather of order 7 with 12 real parameters. We obtain new families of quasi-rational solutions of the NLS equation. With this method, we construct new patterns of different types of rogue waves. We recover triangular configurations as well as rings isolated. As already seen in the previous studies, one sees appearing for certain values of the parameters, new configurations of concentric rings.
Deformations of third order Peregrine breather solutions of the NLS equation with four parameters
2013
In this paper, we give new solutions of the focusing NLS equation as a quotient of two determinants. This formulation gives in the case of the order 3, new deformations of the Peregrine breather with four parameters. This gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation and to describe the apparition of multi rogue waves. With this method, we construct the analytical expressions of deformations of the Peregrine breather of order N=3 depending on $4$ real parameters and plot different types of rogue waves.
Six-parameters deformations of fourth order Peregrine breather solutions of the NLS equation.
2013
We construct solutions of the focusing NLS equation as a quotient of two determinants. This formulation gives in the case of the order 4, new deformations of the Peregrine breather with 6 real parameters. We construct families of quasi-rational solutions of the NLS equation and describe the apparition of multi rogue waves. With this method, we construct the analytical expressions of deformations of the Peregrine breather of order 4 with 6 real parameters and plot different types of rogue waves.
Eighth order Peregrine breather solution of the NLS equation and their deformations with fourteen parameters.
2014
We construct new families of quasi-rational solutions of the NLS equation of order 8 with 14 real parameters. We obtain new patterns of different types of rogue waves. We recover the triangular configurations as well as rings isolated as found for the lower orders. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.
The fifth order Peregrine breather and its eight-parameters deformations solutions of the NLS equation.
2013
We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.