• Corpus ID: 119158259

$\boldsymbol{Diff_+(S^1)-}$pseudo-differential operators and the Kadomtsev-Petviashvili hierarchy

  title={\$\boldsymbol\{Diff\_+(S^1)-\}\$pseudo-differential operators and the Kadomtsev-Petviashvili hierarchy},
  author={Jean-Pierre Magnot and Enrique G. Reyes},
  journal={arXiv: Mathematical Physics},
We establish a non-formal link between the structure of the group of Fourier integral operators $Cl^{0,*}_{odd}(S^1,V)\rtimes Diff_+(S^1)$ and the solutions of the Kadomtsev-Petviashvili hierarchy, using infinite-dimensional groups of series of non-formal pseudo-differential operators. 
1 Citations

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We present explicit formal solutions to the systems of equations in two independent variables $t_m$, $x$, $m =1,2,\dots$, of the Kadomtsev-Petviashvili hierarchy. The main tools used are a

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We recall the notions of Frölicher and diffeological spaces, and we build regular Frölicher Lie groups and Lie algebras of formal pseudo-differential operators in one independent variable. Combining

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  • Jean-Pierre Magnot
  • Mathematics
    International Journal of Geometric Methods in Modern Physics
  • 2013
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