This book studies the large-time asymptotic behavior of solutions
of the pure initial value problem for linear dispersive equations
with constant coefficients and homogeneous symbols in one space
dimension. Complete matched and uniformly-valid asymptotic
expansions are obtained and sharp error estimates are proved. Using
the method of steepest descent much new information on the
regularity and spatial asymptotics of the solutions are also
obtained. Applications to nonlinear dispersive equations are
discussed. This monograph is intended for researchers and graduate
students of partial differential equations. Familiarity with basic
asymptotic, complex and Fourier analysis is assumed.
General
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