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- W2323224169 abstract "Recent theoretical developments in the study of initial-boundary value problems for linear and nonlinear equations have motivated further studies of interface problems for PDEs posed on networks. We investigate the scattering (transmission and reflection) of pulses at interfaces and at bifurcations for the nonlinear Schrodinger (NLS) equation, as a prototype model for bidirectional wave propagation in physical media. NLS equation belongs to an entire class of nonlinear models, called integrable models, for which an intimate relationship exists between their solutions and the compatibility of a linear system (known as the scattering problem). Numerical simulations of such models posed on net- works indicate that, even when the underlying equations are genuinely nonlinear, scattering at junctions still occurs in a linear fashion. This is consistent with similar behavior observed in other nonlinear systems." @default.
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- W2323224169 date "2010-01-01" @default.
- W2323224169 modified "2023-09-27" @default.
- W2323224169 title "Linear and Nonlinear Schrodinger Equations on Simple Networks" @default.
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