Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
We have recently solved the inverse spectral problem for integrable partial differential equations (PDEs) in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter λ. The associated inverse problem, in particular, can be formulated as a nonlinear Riemann–Hilbert (NRH) problem on a given contour of …