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math-ph2009★ 6 cited
Semiclassical limit of the scattering transform for the focusing Nonlinear Schr\" odinger Equation
Alexander Tovbis, Stephanos Venakides
The semiclassical limit of the focusing Nonlinear (cubic) Schr\" odinger Equation (NLS) corresponds to the singularly perturbed Zakharov Shabat (ZS) system that defines the direct…
math-ph2009★ 18 cited
Nonlinear steepest descent asymptotics for semiclassical limit of integrable systems: Continuation in the parameter space
Alexander Tovbis, Stephanos Venakides
The initial value problem of an integrable system, such as the Nonlinear Schr\" odinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to…