Patterns of deformations of Peregrine breather of order 3 and 4 solutions to the NLS equation with multi parameters
الموضوعات : Journal of Theoretical and Applied PhysicsPierre Gaillard 1 , Mickaël Gastineau 2
1 - Université de Bourgogne
2 - IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités UPMC Univ
الکلمات المفتاحية: NLS equation, Peregrine breathers, Rogue waves,
ملخص المقالة :
AbstractIn 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.
