115 citations · 520 across the 14 of their papers we have counts for
4 papers · 2 filters
On the dressing method for Dunajski anti-self-duality equation
L. V. Bogdanov, V. S. Dryuma, S. V. Manakov
A dressing scheme applicable to Dunajski equation is developed. Simple example of constructing solutions in terms of implicit functions is considered. Dunajski equation hierarchy i…
A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields
S. V. Manakov, P. M. Santini
We introduce a hierarchy of integrable PDEs in 2+1 dimensions arising from the commutation of 2-dimensional vector fields. We also solve the associated Cauchy problems, using the r…
Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
S. V. Manakov, P. M. Santini
We solve the inverse scattering problem for multidimensional vector fields and we use this result to construct the formal solution of the Cauchy problem for the second heavenly equ…
The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation
S. V. Manakov, P. M. Santini
We construct the formal solution of the Cauchy problem for the dispersionless Kadomtsev - Petviashvili equation as application of the Inverse Scattering Transform for the vector fi…