/* Last updated: September 8, 2020 by Hereman in Boulder */

/* Data file s-NLS-run2-Sep8-2020.dat for the Nonlinear Schrodinger (NLS) equation. */

/* NLS equation : i u_t + u_xx + a*|u|^2 u = 0 */
/* Set u = u[1] + i u[2], split in real and imaginary parts gives the system: */
/*  u[1]_t + u[2]_xx + a*(u[1]^2+u[2]^2) u[2] = 0, */
/*  u[2]_t - u[1]_xx - a*(u[1]^2+u[2]^2) u[1] = 0. */
/* Assign x[1] to x, x[2] to t, a is a real parameter to capture the focusing and defocusing NLS eqs. */
 
/* number of independent variables: */
p : 2 $

/* number of dependent variables: */
q : 2 $

/* number of equations in the system: */
m : 2 $

parameters:[a]$
sublisteqs:[all]$
subst_deriv_of_vi:true$
highest_derivatives:all$
warnings:true$

/* information is given this time. */
info_given : true$

depends([eta1,f2,f3,f4,f6],[x[1],x[2]]);
depends([f1,f5],x[2]);
depends(eta2,x[2]);
depends([g1,g2],x[2]);

gradef(eta1,x[2],-2*diff(f2,x[1]));
gradef(eta1,x[1],2*f1+g1);
gradef(eta2,x[2],4*f1+2*g1);

f4 : -f2;
f5 : f1;

eta1 : (2*f1+g1)*x[1]+g2;
phi1: f1*u[1]+f2*u[2]+f3; 
phi2: f4*u[1]+f5*u[2]+f6; 

e1 : u[1,[0,1]]+a*(u[1]^2+u[2]^2)*u[2]+u[2,[2,0]];
e2 : u[2,[0,1]]-a*(u[1]^2+u[2]^2)*u[1]-u[1,[2,0]];

v1 : u[1,[0,1]];
v2 : u[2,[0,1]];

/* end of command file s-NLS-run2-Sep8-2020.dat */