(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Akhmediev, Nail; Ankiewicz, Adrian; Amiranashvili, Shalva; Bandelow, Uwe
Evolution equations such as the nonlinear Schrödinger equation (NLSE)
can be extended to include an infinite number of free parameters. The
extensions are not unique. We give two examples that contain the NLSE as the
lowest-order PDE of each set. Such representations provide the advantage of
modelling a larger variety of physical problems due to the presence of an
infinite number of higher-order terms in this equation with an infinite
number of arbitrary parameters. An example of a rogue wave solution for one
of these cases is presented, demonstrating the power of the technique.
