/* Last updated: December 19, 2020 by Hereman in Boulder */
/* For use with symmgrp2020.max under Maxima */

/* File name: Fokker-Planck-Kolmogorov-run3-generic-Dec19-2020-wh.dat. */
/* Data file for the Fokker-Planck-Kolmogorov equation with varying coefficient given in the online manuscript Faruk Gungor. */

/* In this generic case we compute the principal symmetry group which would be valid for any pp(x) */
/* The info below is based on the determining equations obtained in Run 1 */

/* u_t - u_xx + pp(x) u_y = 0 */
/* Assign u[1] to u, x[1] to x, x[2] to y, and x[3] to t, pp is a function of x only. */

/* 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 give in this run. */
info_given : true$

/* careful the symbol p is reserved for the number of independent variables. So, use pp instead. */
depends(pp,x[1]);

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

/* In this generic case we compute the principal symmetry group which would be valid for any pp(x). */

/* Software should confirm again that f2 must satisfy the given PDE */
/* f2 satisfies the Fokker-Planck-Kolmogorov equation itself -- determining an infinite symmetry */
/* gradef(f2,x[3],-pp*diff(f2,x[2])+diff(f2,x[1],2)); */

/* Taking the determining equations from Run 1, we split by powers of pp and set the coefficients of derivatives also equal to zero. */
/* We solved this by hand. We just test the result here. */
/* This is based on the results of Run 1. We are not using: */
/* eta1 : -(pp^2/diff(pp,x[1]))*diff(eta3,x[2])-(pp/diff(pp,x[1]))*(diff(eta3,x[3])-diff(eta2,x[2]))+(1/diff(pp,x[1]))*diff(eta2,x[3]); */
/* Result for the generic case, i.e., for any function pp(x) : */

eta1 : 0;
eta2 : c2;
eta3 : c1;
f1 : c3;

phi1 : f1*u[1]+f2;

e1 : u[1,[0,0,1]] - u[1,[2,0,0]] + pp*u[1,[0,1,0]];
/* pp is function of x only */
v1 : u[1,[0,0,1]];

/* end of data file Fokker-Planck-Kolmogorov-run3-generic-Dec19-2020-wh.dat. */