22 research outputs found
Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
Full text linkWe apply the method of nonlinear steepest descent to compute the long-time
asymptotics of the Korteweg-de Vries equation for decaying initial data in the
soliton and similarity region. This paper can be viewed as an expository
introduction to this method.Comment: 31 page
Continuum Integrals and the Asymptotic Behavior of the Solutions of Parabolic Equations as t→0. Applications to Diffraction
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On asymptotic stability of solitary waves in discrete Klein–Gordon equation coupled to a nonlinear oscillator
No full textA trace formula for differential operators of arbitrary order
No full textAn operator H = H0 +V where H0 = i (N is arbitrary) and V is a differential operator of order N-1 with coefficients decaying sufficiently rapidly at infinity is considered in the space H2(R). The goal of the paper is to find an expression for the trace of the difference of the resolvents (H) -1 and (H0 - z) -1 in terms of the Wronskian of appropriate solutions to the differential equation Hu = zu. This also leads to a representation for the perturbation determinant of the pair H0H
Stable blow‐up dynamics in the ‐critical and ‐supercritical generalized Hartree equation
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