# Integrable systems in 4D associated with sixfolds in Gr(4,6)

@article{Doubrov2017IntegrableSI, title={Integrable systems in 4D associated with sixfolds in Gr(4,6)}, author={B. Doubrov and E. Ferapontov and B. Kruglikov and V. Novikov}, journal={arXiv: Exactly Solvable and Integrable Systems}, year={2017} }

Let $Gr(d,n)$ be the Grassmannian of $d$-dimensional linear subspaces of an $n$-dimensional vector space $V$. A submanifold $X\subset Gr(d, n)$ gives rise to a differential system $\Sigma(X)$ that governs $d$-dimensional submanifolds of $V$ whose Gaussian image is contained in $X$. We investigate a special case of this construction where $X$ is a sixfold in $Gr(4, 6)$. The corresponding system $\Sigma(X)$ reduces to a pair of first-order PDEs for 2 functions of 4 independent variables… Expand

#### 4 Citations

On the algebra of nonlocal symmetries for the 4D Mart\'{\i}nez Alonso-Shabat equation.

- Mathematics, Physics
- 2020

Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property

- Mathematics, Physics
- 2017

Integrability via geometry: Dispersionless differential equations in three and four dimensions

- Mathematics, Physics
- 2016

#### References

SHOWING 1-10 OF 35 REFERENCES

On the integrability in Grassmann geometries: integrable systems associated with fourfolds Gr(3, 5)

- Mathematics, Physics
- 2015

Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability

- Mathematics, Physics
- 2004

On Linear Degeneracy of Integrable Quasilinear Systems in Higher Dimensions

- Mathematics, Physics
- 2009

Integrability via geometry: Dispersionless differential equations in three and four dimensions

- Mathematics, Physics
- 2016