 
Summary: Positivity Properties and
Uniqueness of Solitary Wave Solutions
of the Intermediate LongWave Equation
J. ALBERT
Department of Mathematics, University of Oklahoma
1. INTRODUCTION
The intermediate long wave (ILW) equation was first proposed in [9] and [12] as a model
equation for long internal gravity waves at the interface between two fluids of different
densities, each of finite depth H. Using the rescaled variables introduced in [12], the ILW
equation can be written in the form
ut + 2uux  (NHu)x +
1
H
ux = 0, (1.1)
where the "dispersion operator" NH is the Fourier multiplier operator defined by
(NHu) (k) = (k coth kH)^u(k).
(Here and throughout the paper, circumflexes are used to denote Fourier transforms in
the x variable: thus ^u(k, t) denotes

