Abstract Equations like the Korteweg-de Vries equation (KdV) and modified (mKdV) equation support rogue waves, but the central rogue wave formations come with tails that extend to infinity. The nonlinear diffusion equation has some solutions which are limited in the transverse direction, and the regular definition would seem to exclude having a finite volume, even for the linear parameter. Thus at first, these features would seem to preclude characterizing these by defining suitable finite volumes, but we demonstrate that, with some care, this can be done for these and other physically-relevant equations. Measuring volumes can then allow determination of physical parameters and orders of rogue waves.
Adrian Ankiewicz (Wed,) studied this question.