Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations
| dc.creator | Joshi, Nalini | |
| dc.creator | Petersen, Johannes A. | |
| dc.creator | Schubert, Luke M. | |
| dc.date | 1999-05-20 | |
| dc.date.accessioned | 2026-07-07T06:17:49Z | |
| dc.date.available | 2026-07-07T06:17:49Z | |
| dc.description | We study characteristic Cauchy problems for the Korteweg-deVries (KdV) equation $u_t=uu_x+u_{xxx}$, and the Kadomtsev-Petviashvili (KP) equation $u_{yy}=\bigl(u_{xxx}+uu_x+u_t\bigr)_x$ with holomorphic initial data possessing nonnegative Taylor coefficients around the origin. For the KdV equation with initial value $u(0,x)=u_0(x)$, we show that there is no solution holomorphic in any neighbourhood of $(t,x)=(0,0)$ in ${\mathbb C}^2$ unless $u_0(x)=a_0+a_1x$. This also furnishes a nonexistence result for a class of $y$-independent solutions of the KP equation. We extend this to $y$-dependent cases by considering initial values given at $y=0$, $u(t,x,0)=u_0(x,t)$, $u_y(t,x,0)=u_1(x,t)$, where the Taylor coefficients of $u_0$ and $u_1$ around $t=0$, $x=0$ are assumed nonnegative. We prove that there is no holomorphic solution around the origin in ${\mathbb C}^3$ unless $u_0$ and $u_1$ are polynomials of degree 2 or lower. | |
| dc.description | 17 pages in LaTeX2e, to appear in Stud. Appl. Math | |
| dc.identifier | https://arxiv.org/abs/solv-int/9905010 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9905010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94521 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations | |
| dc.type | text |