  The structure of the solutions to the one dimensional focusing nonlin-ear
Schr{\"o}dinger equation (NLS) for the order N in terms of quasi rational
functions is given here. We first give the proof that the solutions can be
expressed as a ratio of two wronskians of order 2N and then two determinants by
an exponential depending on t with 2N -- 2 parameters. It also is proved that
for the order N , the solutions can be written as the product of an exponential
depending on t by a quotient of two polynomials of degree N (N + 1) in x and t.
The solutions depend on 2N -- 2 parameters and give when all these parameters
are equal to 0, the analogue of the famous Peregrine breather PN. It is
fundamental to note that in this representation at order N , all these
solutions can be seen as deformations with 2N -- 2 parameters of the famous
Peregrine breather PN. With this method, we already built Peregrine breathers
until order N = 10, and their deformations depending on 2N -- 2 parameters.
