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nlin.SI2001
Asymptotics of semiclassical soliton ensembles: rigorous justification of the WKB approximation
P. D. Miller
Rigorous pointwise asymptotics are established for semiclassical soliton ensembles (SSEs) of the focusing nonlinear Schroedinger equation using techniques of asymptotic analysis of…
nlin.SI2001
An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg-de Vries Solitons
P. D. Miller, S. R. Clarke
Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a li…
nlin.SI2000
Semiclassical Soliton Ensembles for the Focusing Nonlinear Schroedinger Equation
S. Kamvissis, K. T. -R. McLaughlin, P. D. Miller
We present a new generalization of the steepest descent method introduced by Deift and Zhou for matrix Riemann-Hilbert problems and use it to study the semiclassical limit of the f…