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Highlights from
An Introduction to the Mathematical Theory of Waves

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An Introduction to the Mathematical Theory of Waves

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20 Aug 2002 (Updated )

Companion Software

kdv2(x,t)
function u = kdv2(x,t)
%KDV2 - Korteweg-de Vries Double Soliton Function
%
%       kdv2(x,t) computes the value u(x,t) of an interacting 
%       double soliton solution of the KdV equation 
%
%            u_t - uu_x + u_xxx = 0
%
%       the KdV equation. t is a scalar and x is a scalar or
%       a vector.  

% Created: 6/95 by R. Knobel

% Parameters k1,k2,eta1,eta2 can be adjusted to alter
% the speeds and amplitudes of the double soliton

k1 = 1;
k2 = 2;
eta1 = 0;
eta2 = 0;

%
A    = ( (k1-k2)/(k1+k2) )^2;
w1   = k1^3;
w2   = k2^3;
phi1 = exp(w1*t - k1*x + eta1);
phi2 = exp(w2*t - k2*x + eta2);

u = 2*(k1^2 * phi1 + k2^2 * phi2 + 2*(k1-k2)^2*phi1.*phi2 + ...
    A*(k2^2 * phi1 + k1^2 + phi2) .* phi1 .* phi2) ./ ...
    (1+phi1+phi2+A.*phi1.*phi2).^2;


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