جوابهای تحلیلی معادله غیرخطی شرودینگر

clc
clear all
t0=2; % [ps] initial pulse width
beta2 = -20; % [ps²km^-1] the group-velocity dispersion parameter (GVD)
gama= 2; % [W^-1km^-1] nonlinear parameter (SPM)
E0 = (1/t0)*sqrt(abs(beta2)/gama); % [W^(1/2)] initial amplitude
 

%N = 1; firs-order soliton
[x,y]=meshgrid(0:.03:1.5,5.5:-.03:-5.5);
u=E0*sech(y).*exp(i*x/2);
z=(conj(u)).*(u);
mesh(x,y,z)
axis tight
view(-60,40)
 

%N = 2; second-order soliton
[x,y]=meshgrid(0:.03:1.5,-2.8:.03:2.8);
G2=cosh(3*y)+3*cosh(y).*exp(i*4*x);
H2=cosh(4*y)+4*cosh(2*y)+3*cos(4*x);
u=4*E0*exp(i*x).*G2./H2;
z=(conj(u)).*(u);
figure
mesh(x,y,z)
axis tight
view(-60,40)
 

%N = 3; third-order soliton
[x,y]=meshgrid(0:.03:1.5,-2.8:.03:2.8);
G3=2*cosh(8*y)+32*cosh(2*y)+...
    exp(i*4*x).*(36*cosh(4*y)+16*cosh(6*y))+...
    exp(i*12*x).*(20*cosh(4*y)+80*cosh(2*y))+...
    5*exp(-i*8*x)+45*exp(i*8*x)+20*exp(i*16*x);

H3=cosh(9*y)+9*cosh(7*y)+...
    64*cosh(3*y)+36*cosh(y)+...
    36*cosh(5*y).*cos(4*x)+...
    20*cosh(3*y).*cos(12*x)+...
    90*cosh(y).*cos(8*x);
 

u=3*E0*exp(i*x/2).*G3./H3;
z=(conj(u)).*(u);
figure
mesh(x,y,z)
axis tight
view(-60,40)

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Reference

S. Lopez-Aguayo, J.P. Ochoa-Ricoux, and J.C. Gutierrez-Vega "Exploring the behavior of solitons on a desktop personal computer" REVISTA MEXICANA DE FISICA E 52 (1) 28–36.