6533b7d8fe1ef96bd126961a

RESEARCH PRODUCT

Deformations of third order Peregrine breather solutions of the NLS equation with four parameters

Pierre Gaillard

subject

NLS equationAkhmediev's solutions.Nonlinear 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]Riemann theta functionsAkhmediev's solutions[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Nonlinear Sciences::Pattern Formation and SolitonsFredholm determinants

description

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.

yearjournalcountryeditionlanguage
2013-02-01
https://hal.science/hal-00783882