Explicit Quasi-Rational Solutions and Parameter-Dependent Patterns for the Fifth Equation of the NLS Hierarchy
Pierre Gaillard *
Universite de Bourgogne Franche Comte, Institut de Mathematiques de Bourgogne, 9 Avenue Alain Savary BP 47870, 21078 Dijon Cedex, France.
*Author to whom correspondence should be addressed.
Abstract
This study is part of a research program of rational solutions of the hierarchy of the nonlinear Schrodinger equation.
Here, we are interested in the equation of order 5 and we construct explicitly the first orders of rogue waves which were not yet found.
In particular, quasi rational solutions to the fifth equation of the NLS hierarchy are constructed. We give explicit expressions of these solutions for the first orders depending on multi-parameters. We study the patterns of these solutions in the (x, t) plane according to the different values of the parameters.
Keywords: Equation of order of the NLS hierarchy, rational solutions, rogue waves