6533b7d8fe1ef96bd126959c
RESEARCH PRODUCT
Deformations of higher order Peregrine breathers and monstrous polynomials.
Pierre Gaillardsubject
NLS equationNonlinear Sciences::Exactly Solvable and Integrable Systems[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]WronskiansPeregrine breathers[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Peregrine breathers.[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Nonlinear Sciences::Pattern Formation and Solitonsdescription
International audience; In the following, we present two new results about the focusing one dimensional NLS equation : 1. We construct solutions of NLS equation in terms of wronskians. Then performing a special passage to the limit when a parameter tends to 0, we obtain quasi-rational solutions of NLS equation. 2. We construct quasi-rational solutions in terms of determinants without of a limit. Which is new is that we obtain at order N, solutions depending on 2N-2 parameters. 3. When all these parameters are equal to zeros, we recover Peregrine breathers; it is the reason why we call these solutions deformations of Peregrine breathers. \\ Then we deduce new patterns of solutions in the (x,t) plane for the orders N=3 to N=10.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-06-11 |