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RESEARCH PRODUCT
Patterns of deformations of P 3 and P 4 breathers solutions to the NLS equation
Pierre GaillardMickaël Gastineausubject
NLS equationPeregrine breather[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph][ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]rogue waves[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]description
In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a quotient of two determinants by an exponential depending on t. This formulation gives in the case of the order 3 and 4, solutions with respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-02-19 |