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

@article{Magnot2018boldsymbolDiff\_S1pseudodifferential, 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}, year={2018} }

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.

## One Citation

### On the geometry of $Diff(S^1)$-pseudodifferential operators based on renormalized traces.

- Mathematics
- 2020

In this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of Dif f (S 1) with a group of classical pseudo-differential operators of any order.…

## References

SHOWING 1-10 OF 53 REFERENCES

### The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups

- Mathematics
- 2013

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 …

### The Cauchy problem of the Kadomtsev-Petviashvili hierarchy with arbitrary coefficient algebra

- Mathematics
- 2017

Mulase solved the Cauchy problem of the Kadomtsev-Petviashvili (KP) hierarchy in an algebraic category in “Solvability of the super KP equation and a generalization of the Birkhoff decomposition”…

### Well-Posedness of the Kadomtsev–Petviashvili Hierarchy, Mulase Factorization, and Frölicher Lie Groups

- MathematicsAnnales Henri Poincaré
- 2020

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…

### Determinants of elliptic pseudo-differential operators

- Mathematics
- 1994

Determinants of invertible pseudo-differential operators (PDOs) close to positive self-adjoint ones are defined throughthe zeta-function regularization. We define a multiplicative anomaly as the…

### Solitons : differential equations, symmetries and infinite dimensional algebras

- Mathematics
- 2000

Preface 1. The KdV equation and its symmetries 2. The KdV hierarchy 3. The Hirota equation and vertex operators 4. The calculus of Fermions 5. The Boson-Fermion correspondence 6. Transformation…

### AMBROSE–SINGER THEOREM ON DIFFEOLOGICAL BUNDLES AND COMPLETE INTEGRABILITY OF THE KP EQUATION

- MathematicsInternational Journal of Geometric Methods in Modern Physics
- 2013

In this paper, we start from an extension of the notion of holonomy on diffeological bundles, reformulate the notion of regular Lie group or Frölicher Lie groups, state an Ambrose–Singer theorem that…

### Chern Forms on Mapping Spaces

- Mathematics
- 2006

We state a Chern–Weil type theorem which is a generalization of a Chern–Weil type theorem for Fredholm structures stated by Freed in [4]. Using this result, we investigate Chern forms on based…

### Geometry of determinants of elliptic operators

- Mathematics
- 1995

D.B. Ray and I.M. Singer invented zeta-regularized determinants for positive definite elliptic pseudo-differential operators (PDOs) of positive orders acting in the space of smooth sections of a…