Tenth Peregrine breather solution to the NLS equation

{In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P-10 breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer co-efficients times trivial exponential factor. This formula drastically simplifies for the ``initial values'' namely for t = 0 or x = 0. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x = 0