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Note on Generating Nonlinear Evolution Equations
SIAM Journal on Applied Mathematics, 1976Two techniques for generating nonlinear evolution equations which can be analyzed by the inverse-scattering method are shown to be equivalent in general.
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Some Higher‐Order Nonlinear Evolution Equations
Studies in Applied Mathematics, 1975Nonlinear evolution equations are generated which correspond to isospectral differential‐matrix eigenvalue problems. Although not discussed here, this procedure is appropriate for the analysis of the initial‐value solution by the inverse‐scattering method. In the 2 × 2 case the results obtained are consistent with other more general procedures.
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Some Nonlinear Evolution Equations
1983In this section we will study the following semilinear initial value problem: $$\left\{ {\begin{array}{*{20}{c}} {\frac{{du(t)}}{{dt}} + Au(t) = f(t,u(t)), t > {{t}_{0}}} \hfill \\ {u({{t}_{0}}) = {{u}_{0}}} \hfill \\ \end{array} } \right.$$ (1.1) where -A is the infinitesimal generator of a C0semigroup T(t), t ≥ 0, on a Banach space X and f:
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Solitons, Nonlinear Evolution Equations and Inverse Scattering
, 1992M. Ablowitz, Peter A. Clarkson
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