# Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws

@article{Lou2022DeformationCD, title={Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws}, author={S. Y. Lou and Xia Hao and Man Jia}, journal={Journal of High Energy Physics}, year={2022}, volume={2023}, pages={1-14} }

Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm. The algorithm can be applied to Lax pairs and higher order flows. In other words, if the original lower dimensional model is Lax integrable (possesses Lax pairs) and symmetry integrable (possesses infinitely many higher order symmetries and/or infinitely many conservation laws), then the…

## 2 Citations

### Multidimensional Integrable Deformations of Integrable PDEs

- Mathematics
- 2023

In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimensional systems. We…

### Higher dimensional integrable deformations of the modified KdV equation

- Mathematics, PhysicsCommunications in Theoretical Physics
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The derivation of nonlinear integrable evolution partial differential equations in higher dimension has always been the holy grail in the field of integrability. The well-known modified KdV…

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