Patterns of deformations of Peregrine breather of order 3 and 4 solutions to the NLS equation with multi parameters

In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing schro¨dinger 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.