01177nas a2200145   4500008004100000245008600041210006900127300001300196490000800209520068400217100001800901700002100919700002100940856007000961       2018                        eng d00aNumerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves0 aNumerical study of the KadomtsevPetviashvili equation and disper  a201704580 v4743 a<p>A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.</p>1 aGrava, Tamara1 aKlein, Christian1 aPitton, Giuseppe  uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458