second_order_soliton(tau,zeta)

%SECOND_ORDER_SOLITON Return a second-order soliton of the nlse.
%
%   Return the field distribution of a second-order soliton of the NLSE, as
%   a function of local time and distance.  Such solitons are often known
%   as 'breathers'.
%
%     U = SECOND_ORDER_SOLITON(TAU,Z);
%
%   See also: GAFFE_DEMO_SOLITON


% $Author: graceej $ $Date: 2010/05/22 20:58:36 $
% $Revision: 1.1 $


% Copyright (c) 2010, Edward J. Grace
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function u = second_order_soliton(tau,zeta)
soliton_numerator = (4.*(cosh(3.*tau) + 3.*exp(4.*i.*zeta).*cosh(tau)).*exp(i.*zeta./2.0));
soliton_denominator = (cosh(4.*tau) + 4.*cosh(2.*tau) + 3.*cos(4.*zeta));
% @bug Fix for limits formally using l'Hopital etc. this is a quick and
% dirty.
u=soliton_numerator./soliton_denominator;
u(isnan(u))=0;
end