Integral relations for rogue wave formations of Gardner equation

Abstract

Rogue wave structures can often be described by a set of rational solutions. These can be derived for physical systems satisfying various well-known nonlinear equations. We present integral relations which characterize the Gardner rogue waves, and show that they take integer values. These could be used to identify the order of a measured rogue wave. Finally, we compare these with rogue wave forms of other nonlinear partial differential equations. Similarities and differences in integral relations among those systems are found. We study the movement of relevant poles on the complex plane as well.