Nonhomogeneous Dispersive Water Waves and Painlev\'{e} equations

Abstract

In this letter we consider three nonhomogeneous deformations of Dispersive Water Wave (DWW) soliton equation and prove that their stationary flows are equivalent to three famous Painlev\'{e} equations, i.e. $P_{II}$, $P_{III}$ and $P_{IV},$ respectively.

Keywords

• nonlinear sciences - exactly solvable and integrable systems
• mathematics - analysis of pdes