The solutions to the one dimensional focusing nonlinear Schrodinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N + 1) in x and t. These solutions depend on 2N - 2 parameters: when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call P_N breathers. Between all quasi-rational solutions of rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at point (x = 0, t = 0), the P_N breather is distinguished by the fact that P_N(0, 0) = 2N + 1. We construct Peregrine breathers of the rank N explicitly for N ≤ 11. We give figures of these P_N breathers in the (x; t) plane; plots of the solutions P_N(0; t), P_N(x; 0), never given for 6 ≤ N ≤ 11 are constructed in this work. It is the first time that the Peregrine breather of order 11 is explicitly constructed.
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