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Nonlinear Evolution Equations—Continuous and Discrete
SIAM Review, 1977An important recent advance in nonlinear wave motion has been the discovery of a method of solution to a class of nonlinear evolution equations. The technique relies on a relation between the evolution equation, and an associated linear eigenvalue (scattering) problem. The initial value solution is found by the method of inverse scattering.
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Antidark solitons and soliton molecules in a (3 + 1)-dimensional nonlinear evolution equation
Nonlinear dynamics, 2020Xin Wang, Jiao Wei
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Wazewski’s method for nonlinear evolution equations
Mathematical Notes, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Rational solutions for a (3+1)-dimensional nonlinear evolution equation
Communications in nonlinear science & numerical simulation, 2020Xin Wang, Jiao Wei, X. Geng
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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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