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On the Inverse Scattering Transform for the Kadomtsev‐Petviashvili Equation
Author(s) -
Ablowitz M. J.,
Yaacov D. Bar,
Fokas A. S.
Publication year - 1983
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1983692135
Subject(s) - eigenfunction , mathematics , inverse scattering transform , inverse scattering problem , mathematical analysis , sign (mathematics) , bounded function , boundary value problem , inverse problem , inverse , integral equation , eigenvalues and eigenvectors , physics , geometry , quantum mechanics
The initial value problem of the Kadomtsev‐Petviashvili equation for one choice of sign in the equation has been recently investigated in the literature. Here we consider the other choice of sign. We introduce suitable eigenfunctions which though bounded are not analytic in the spectral parameter. This, in contrast to the known case, prevents us from formulating the inverse problem as a nonlocal Riemann‐Hilbert boundary value problem. Nevertheless a suitable formulation is given and a formal solution is constructed via a linear integral equation.