94 citations · 181 across the 6 of their papers we have counts for
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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…
On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
S. V. Manakov, P. M. Santini
We make use of the nonlinear Riemann Hilbert problem of the dispersionless Kadomtsev Petviashvili equation, i) to construct the longtime behaviour of the solutions of its Cauchy pr…
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…
An integrable generalization of the Toda law to the square lattice
P. M. Santini, M. Nieszporski, A. Doliwa
We generalize the Toda lattice (or Toda chain) equation to the square lattice; i.e., we construct an integrable nonlinear equation, for a scalar field taking values on the square l…
Initial-boundary value problems for linear PDEs: the analyticity approach
A. Degasperis, S. V. Manakov, P. M. Santini
To study initial-boundary value problems for linear PDEs we have recently proposed two alternative approaches in Fourier space: the "analyticity appoach" and the "elimination by re…
Initial-Boundary Value Problems for Linear and Soliton PDEs
A. Degasperis, S. V. Manakov, P. M. Santini
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectra…