Generic
Number  1281 
References
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Written
Date 
September 20th, 11 
Modified
Date 
September 20th, 11 
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Summary 
A special system of partial differential equations (PDEs) occur in a natural way
while studying a class of irrotational inviscid fluid
flow problems involving infinite channels. Certain aspects of solutions of
such PDEs are analyzed in the context of flow problems involving multiple
layers of fluids of different constant densities in a channel associated with
arbitrary bottom topography. The whole analysis is divided into two parts
part A and part B. In part A the linearized theory is employed along with
the standard Fourier analysis to understand such flow problems and phys
ical quantities of interest are derived analytically. In part B, the same set
of problems handled in part A are examined in the light of a weakly non
linear theory involving perturbation in terms of a small parameter and it
is shown that the original problems can be cast into KdV type of nonlinear
PDEs involving the bottom topography occurring in one of the coeffcients
of these equations. Special cases of bottom topography are worked out in detail and
expressions for quantities of physical importance are derived. 
