115 citations · 520 across the 14 of their papers we have counts for
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Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
S. V. Manakov, P. M. Santini
We review some results about the theory of integrable dispersionless PDEs arising as commutation condition of pairs of one-parameter families of vector fields, developed by the aut…
Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
S. V. Manakov, P. M. Santini
We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral pa…
On the dispersionless Kadomtsev-Petviashvili equation in n+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking
S. V. Manakov, P. M. Santini
We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quas…
On the solutions of the second heavenly and Pavlov equations
S. V. Manakov, P. M. Santini
We have recently solved the inverse scattering problem for one parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for…
The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
S. V. Manakov, P. M. Santini
We have recently solved the inverse spectral problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a…
Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
L. V. Bogdanov, V. S. Dryuma, S. V. Manakov
Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to Dunajski equation is developed, an example of constructing solutions in terms of…