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Strong Coupling Limit of Certain Multidimensional Nonlinear Wave Equations
Author(s) -
Ablowitz Mark J.,
Schultz Cherie L.
Publication year - 1989
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/sapm1989803229
Subject(s) - nonlinear system , inverse scattering transform , limit (mathematics) , mathematics , mathematical analysis , action (physics) , inverse , perturbation (astronomy) , scattering , quantum , coupling (piping) , inverse scattering problem , initial value problem , inverse problem , physics , mathematical physics , quantum mechanics , geometry , mechanical engineering , engineering
A class of multidimensional nonlinear evolution equations of physical interest are considered in the limit of strong coupling. It turns out that the initial value solution is readily obtained. In the special case of the Davey‐Stewartson equation the inverse scattering transform is shown to reduce to the obtained solution via perturbation. A number of other features are discussed as well, such as action angle variables, periodic solutions, and quantum analogues.