OICC Press Journal of Theoretical and Applied Physics 2251-7235 7 1 2023 11 17 Two-parameter determinant representation of seventh order rogue wave solutions of the NLS equation 10.1186/2251-7235-7-45 EN Pierre Gaillard Universit ́e de Bourgogne Franche Comt ́e, Institut de math ́ematiques de Bourgogne, Dijon Cedex, France Journal Article 2023 11 17 AbstractWe present a new representation of solutions of focusing nonlinear Schrödinger equation (NLS) equation as a quotient of two determinants. We construct families of quasi-rational solutions of the NLS equation depending on two parameters, a and b. We construct, for the first time, analytical expressions of Peregrine breather of order 7 and multi-rogue waves by deformation of parameters. These expressions make possible to understand the behavior of the solutions. In the case of the Peregrine breather of order 7, it is shown for great values of parameters a or b the appearance of the Peregrine breather of order 5.PACS35Q55; 37K10