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nlin.SI2010★ 22 cited
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…
nlin.SI2010★ 27 cited
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…