@article{Patterns of deformations of Peregrine breather of order 3 and 4 solutions to the NLS equation with multi parameters_2023, volume={10}, url={https://oiccpress.com/journal-of-theoretical-and-applied-physics/article/patterns-of-deformations-of-peregrine-breather-of-order-3-and-4-solutions-to-the-nls-equation-with-multi-parameters/}, DOI={10.1007/s40094-015-0204-6}, abstractNote={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.}, number={2}, journal={Journal of Theoretical and Applied Physics}, publisher={OICC Press}, year={2023}, month={Nov.}, keywords={NLS equation, Peregrine breathers, Rogue waves} }