If I further simplify this, that will give me, that d square eta d x square plus one by x d
eta by d x plus k square eta equal to zero. So this is the case, this is the equation of long
wave. And for a channel, where the width is varying, here the death is constant, and with
h varying like this; e channel in h. And it can be seen, that this is a kind of first or zero
third of this equation. We have this is zero third of the Bessel equation, and you know
the solution of this equation is very interesting; that gives me eta x t, because the solution
of this is c naught j naught, or other call it c 1 j naught k x plus c 2 c 1 c 2 y naught k x
into cos omega t, this is the general form of eta. And again as we know that the property
of five naught, as just at near x is equal to at x is equal to zero, y know naught will tend
to infinity, and however we are looking for eta, which solution is bounded at the, where x
is equal to zero, so that it shows that, it will say that c 2 has to be zero. So the process we
get eta equal to c 0 c 1 j naught k x into cos omega t.