6533b7d2fe1ef96bd125dd83

RESEARCH PRODUCT

Six-parameters deformations of fourth order Peregrine breather solutions of the NLS equation.

Pierre Gaillard

subject

NLS equationAkhmediev's solutions.Nonlinear Sciences::Exactly Solvable and Integrable Systemswronskians[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Fredohlm determinantsPeregrine 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 Solitons

description

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.

https://hal.archives-ouvertes.fr/hal-00798669v2/file/halnlsN4P6SOL1-4FIG1-3V5JMP.pdf