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

/* Data file s-Karpman-run4-Sep8-2020.dat for Karpman's equations: */

/* Equations and a solution strategy are given in: */
/* B. Champagne, W. Hereman, and P. Winternitz, */
/* The computer calculation of Lie point symmetries of large systems of differential equations, */
/* Computer Physics Communications, 66(2-3), 319-340 (1991). */
/* DOI: 10.1016/0010-4655(91)90080-5. */

parameters:[s1,s2,w1,w2,a1,a2]; 
/* working with all equations */
sublisteqs:[all];
/* working with all derivatives */
highest_derivatives:all;
warnings:true;
subst_deriv_of_vi:true;
/* information is given now  */
info_given : true$

p:4;
q:3;
m:3;

depends([eta1,eta2,eta3,f1,f2],[x[1],x[2],x[3],x[4]]);
depends(eta4,x[4]);
depends(phi1,[x[1],x[2],x[3],x[4],u[1]]);
depends(phi2,[x[1],x[2],x[3],x[4],u[2]]);
depends(phi3,[x[1],x[2],x[3],x[4],u[1],u[2],u[3]]);

phi1 : f1*u[1];
phi2 : (2*diff(eta1,x[1])-diff(eta4,x[4]))*u[2]+f2;

gradef(eta3,x[1],-(s2/s1)*diff(eta1,x[3]));
gradef(eta3,x[2],-(s2/s1)*diff(eta2,x[3]));
gradef(eta2,x[1],-diff(eta1,x[2]));
gradef(eta3,x[3],diff(eta1,x[1]));
gradef(eta2,x[2],diff(eta1,x[1]));

e1:u[1,[0,0,0,1]]+w1*u[1,[0,0,1,0]]+1/2*(s1*(2*u[1,[1,0,0,0]]*u[2,[1,0,0,0]]+
   2*u[1,[0,1,0,0]]*u[2,[0,1,0,0]]+u[1]*u[2,[2,0,0,0]]+u[1]*u[2,[0,2,0,0]])+
   s2*(2*u[1,[0,0,1,0]]*u[2,[0,0,1,0]]+u[1]*u[2,[0,0,2,0]]));

e2:u[2,[0,0,0,1]]+w1*u[2,[0,0,1,0]]-1/2*(s1*(u[1,[2,0,0,0]]/u[1]+
   u[1,[0,2,0,0]]/u[1]-u[2,[1,0,0,0]]^2-u[2,[0,1,0,0]]^2)+
   s2*(u[1,[0,0,2,0]]/u[1]-u[2,[0,0,1,0]]^2))+a1*u[3];
 
e3:u[3,[0,0,0,2]]-w2^2*(u[3,[2,0,0,0]]+u[3,[0,2,0,0]]+u[3,[0,0,2,0]])-
   2*a2*u[1]*(u[1,[2,0,0,0]]+u[1,[0,2,0,0]]+u[1,[0,0,2,0]])-
   2*a2*(u[1,[1,0,0,0]]^2+u[1,[0,1,0,0]]^2+u[1,[0,0,1,0]]^2);
 
v1:u[1,[0,0,0,1]];
v2:u[2,[0,0,0,1]];
v3:u[3,[0,0,0,2]];

/* end of data file s-Karpman-run4-Sep8-2020.dat */