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STABILITY OF SOLITARY-WAVE SOLUTIONS TO LONG-WAVE EQUATIONS
 

Summary: STABILITY OF SOLITARY-WAVE
SOLUTIONS TO LONG-WAVE EQUATIONS
WITH GENERAL DISPERSION
John Albert Felipe Linares
1. Introduction
In this report we consider nonlinear dispersive systems of the form
ut + D(f(u) - Mu)x = 0, (1)
where u(x, t) = (u1(x, t), . . . , un(x, t)) is a map from R R to Rn
, D is a
constant diagonal matrix with positive entries, f : Rn
Rn
is nonlinear, and
the dispersion operator M acts as a Fourier multiplier operator in the x variable.
More precisely, for each fixed t, Mu is a vector-valued function defined by
Mu(k, t) = m(k)u(k, t), k R,
where circumflexes denote Fourier transforms with respect to x,
g(k) =
R
e-ikx
g(x) dx.

  

Source: Albert, John - Department of Mathematics, University of Oklahoma

 

Collections: Mathematics