/* Last updated: January 25, 2021 by Hereman in Boulder */
/* For use with symmgrp2020.max under Maxima */

/* File name: p5diffusion-run4-Jan25-2021-wh.dat. */
/* Data file for diffusion equation with power 5 diffusivity given in the online manuscript Faruk Gungor. */

/* u_t - x^5 u_xx + x u_y = 0 */
/* Assign u[1] to u, x[1] to x, x[2] to y, and x[3] to t. */

/* number of independent variables: */
p : 3$

/* number of dependent variables: */
q : 1$

/* number of equations in the system: */
m : 1$

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

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

depends([eta1,f1,f2],[x[1],x[2],x[3]]);
depends([eta2,g1],x[2]);
depends([g2,eta3],[x[2],x[3]]);

/* f2 must satisfy the original equation itself. */
/* We will bring that back only at the end to avoid that this constraint is repeated every time. */
gradef(f2,x[3],x[1]^5*diff(f2,x[1],2)-x[1]*diff(f2,x[2]));

/* f1 must also satisfy the original equation and we need to take that into account in a few runs. */
/* gradef(f1,x[3],x[1]^5*diff(f1,x[1],2)-x[1]*diff(f1,x[2])); */

f1 : -(1/2)*(1/x[1])*diff(g1,x[2],2)-x[1]*diff(g1,x[2])-(3/4)*(x[3]/x[1])*diff(eta2,x[2],3)-(3/2)*x[1]*x[3]*diff(eta2,x[2],2)-(1/(2*x[1]^2))*diff(eta2,x[2],2)+g2;

eta3 : (3/2)*diff(eta2,x[2])*x[3]+g1;

eta1 : -x[1]*diff(eta3,x[3])-x[1]^2*diff(eta3,x[2])+diff(eta2,x[3])+x[1]*diff(eta2,x[2]);

phi1 : f1*u[1]+f2;

e1 : u[1,[0,0,1]]-x[1]^5*u[1,[2,0,0]]+x[1]*u[1,[0,1,0]];
/* eliminate u_t */
v1 : u[1,[0,0,1]];

/* end of data file p5diffusion-run4-Jan25-2021-wh.dat. */