6533b838fe1ef96bd12a39aa
RESEARCH PRODUCT
Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.
Pierre Gaillardsubject
NLS equationNonlinear Sciences::Exactly Solvable and Integrable SystemsWronskians[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Peregrine breathersRogue waves[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Riemann theta functions[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Nonlinear Sciences::Pattern Formation and Solitonsfredholm determinantsAkhmediev's breathersdescription
We present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work is based on a recent paper in which we have constructed a multi-parametric family of this equation in terms of wronskians. This formulation was written in terms of a limit involving a parameter. Here we give a very compact formulation without presence of a limit. This is a completely new result which gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation. With this method, we construct Peregrine breathers of orders N=4 to 7 and multi-rogue waves associated by deformation of parameters.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-09-16 |