The NLS4 equation of the NLS hierarchy and its rational solutions
Résumé
This study concerns the research of rational solutions of the hierarchy of the nonlinear Schrödinger equation. In particular, we are interested in the equation of order 4. Rational solutions to the fourth equation of the NLS hierarchy are constructed and explicit expressions of these solutions are given for the first orders. These soltions depend on multi real parameters. We study the associated patterns of these solutions in the (x, t) plane according to the different values of parameters. This work allows to highlight the phenomenon of rogue waves as in the case of lower order equations such as the nonlinear Schrödinger equation, the mKdV equation or the Hirota equation.
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