We present a new representation of solutions of focusing nonlinear Schr?dinger 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. PACS 35Q55; 37K10
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