Families of quasi-rational solutions of the NLS equation as an extension of higher order Peregrine's solutions.
Résumé
We give a family of solutions of the focusing NLS equation as a product of a quotient of two wronskians of order 2N by an exponential. When we perform a special passage to the limit when all the periods tend to infinity, we get a family of solutions depending on 7N+1 parameters. We give explicit representations of solutions for N=1, 2, 3. As particular cases, we recover the so called higher Peregrine's breathers labeled by the positive integer N.
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