N ov 2 00 6 A hierarchy of integrable PDEs in 2 + 1 dimensions associated with 2-dimensional vector fields

@inproceedings{Manakov2006NO2,
  title={N ov 2 00 6 A hierarchy of integrable PDEs in 2 + 1 dimensions associated with 2-dimensional vector fields},
  author={Sergey V Manakov and Paolo Maria Santini},
  year={2006}
}
We introduce a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for one-parameter families of vector fields recently introduced in [1, 2]. Due to the ring property of the space of eigenfunctions, the inverse problem can be formulated in three distinguished ways; in particular, one formulation… CONTINUE READING

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