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- W1191006670 abstract "This chapter provides an introduction to Zakharov–Shabat inverse scattering. The original ZS-AKNS settings allow only finitely many simple poles, and with some algebraic extension, the case of finitely many multiple poles can also be accommodated. The inverse scattering problem is to construct q from the scattering data v by solving the Riemann–Hilbert problem (RHP). In general, a matrix RHP cannot be solved explicitly (except in the scalar case). However, the considered RHP is equivalent to a Fredholm singular integral equation, which can be used to derive various properties of the inverse scattering transform. The nonlinear Schrödinger (NLS) equation is not the only equation that can be solved by the inverse scattering method (ISM) of ZS-AKNS. In fact, by using different V in the Lax pair, one may solve simultaneously an infinite hierarchy of (independent) evolution equations." @default.
- W1191006670 created "2016-06-24" @default.
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- W1191006670 date "2002-01-01" @default.
- W1191006670 modified "2023-09-23" @default.
- W1191006670 title "Zakharov-Shabat Inverse Scattering" @default.
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- W1191006670 doi "https://doi.org/10.1016/b978-012613760-6/50095-4" @default.
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