Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili
  equations   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.

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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con