Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: PIERRE GAILLARD
Pages: [71] - [153]
Received Date: Received November 27, 2011
Submitted by:
This article contains two basic results. First, we derive a wronskian
representation for the well known multi phase N-periodic
solutions to the focusing NLS equation. Next, we perform a special
passage to the limit when all the periods tend to infinity.
We claim that this provides a new systematic approach for constructing
the so called higher Peregrine breathers labelled by the positive
integer N. We give explicit representations of all higher
Peregrine breathers for 
until to 
and speculate about further extensions.
Riemann theta functions, NLS equation, Fredholm determinant, wronskians, Peregrine breathers, rogue waves.
