In this paper we study the smoothness properties of solutions to the KP-II equation, utx + uxxxx + uxx + uyy + (uux)x = 0, u(x,y,0) = φ(x,y). We show that the equation's dispersive nature leads to a ...
The genus-1 Kadomtsev–Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including ...
Processes in nature can often be described by equations. In many non-trivial cases, it is impossible to find the exact solutions to these equations. However, some equations are much simpler to deal ...
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