Solutions of the Kpi Equation with Smooth Initial Data

Details Solutions of the Kpi Equation with Smooth Initial Data Solutions of the Kpi Equation with Smooth Initial Data

1993-06-30

arxiv.org/abs/solv-int/9306004v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, 23 June 1993, LaTex file

Scientific paper

10.1088/0266-5611/10/3/001

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 $t\not=0$. 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.

Affiliated with

Also associated with

No associations

Rating

Solutions of the Kpi Equation with Smooth Initial Data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Solutions of the Kpi Equation with Smooth Initial Data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solutions of the Kpi Equation with Smooth Initial Data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-345911