6533b82cfe1ef96bd128f1ea
RESEARCH PRODUCT
2N+1 highest amplitude of the modulus of the N-th order AP breather and other 2N-2 parameters solutions to the NLS equation
Pierre Gaillardsubject
Nonlinear Sciences::Exactly Solvable and Integrable Systemsnumbers : 33Q55[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]4710A-[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]37K10[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]4754Bd 1Nonlinear Sciences::Pattern Formation and Solitons33Q55 37K10 47.10A- 47.35.Fg 47.54.Bd4735Fgdescription
We construct here new deformations of the AP breather (Akhmediev-Peregrine breather) of order N (or AP N breather) with 2N −2 real parameters. Other families of quasi-rational solutions of the NLS equation are obtained. We evaluate the highest amplitude of the modulus of AP breather of order N ; we give the proof that the highest amplitude of the AP N breather is equal to 2N + 1. We get new formulas for the solutions of the NLS equation, different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We get the triangular configurations as well as isolated rings at the same time. Moreover, the appearance for certain values of the parameters, of new configurations of concentric rings are underscored.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-03-14 |