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Positivity Properties and Uniqueness of Solitary Wave Solutions
 

Summary: Positivity Properties and
Uniqueness of Solitary Wave Solutions
of the Intermediate Long-Wave 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

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

 

Collections: Mathematics