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- W3104162650 abstract "The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No additional special constraints, usually considered in literature, as $int!dx,u(0,x,y)=0$ are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that $u(t,x,y)$ satisfies a special evolution version of the KPI equation and that, in general, $partial_t u(t,x,y)$ has different left and right limits at the initial time $t=0$. The conditions of the type $int!dx,u(t,x,y)=0$, $int!dx,xu_y(t,x,y)=0$ and so on (first, second, etc. `constraints') are dynamically generated by the evolution equation for $tnot=0$. On the other side $int!dx!!int!dy,u(t,x,y)$ with prescribed order of integrations is not necessarily equal to zero and gives a nontrivial integral of motion." @default.
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- W3104162650 date "1994-06-01" @default.
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- W3104162650 title "Solutions of the KPI equation with smooth initial data" @default.
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