(* d_comkdv.m *)

(* Discretization of the combined KdV-mKdV equation. *)
(* See slides CU-Boulder p. 43 *)

(* Complete equation aa and bb non-zero *)

hh = 1;

(* cc = gamma on slides, aa = alpha, bb = beta, dd = delta *)

u[1][n_]'[t]:= -Expand[(cc+aa*u[1][n][t]+bb*u[1][n][t]^2)*
( dd*((1/2)*u[1][n+2][t]-u[1][n+1][t]+u[1][n-1][t]-(1/2)*u[1][n-2][t])+
(aa/2)*(u[1][n+1][t]^2-u[1][n-1][t]^2+
u[1][n][t]*(u[1][n+1][t]-u[1][n-1][t])+
u[1][n+1][t]*u[1][n+2][t]-u[1][n-1][t]*u[1][n-2][t])+
(bb/2)*(u[1][n+1][t]^2*(u[1][n+2][t]+u[1][n][t])-
u[1][n-1][t]^2*(u[1][n-2][t]+u[1][n][t]) ) ) ];

noeqs = 1;
name = "Herbst/Taha Discretization of combined KdV-mKdV Equation";
parameters = {};
weightpars = {aa,bb,cc,dd};

formrho = 0;

(* densitychoice=1; *)

(* weightu[1] = 1/4; *)

weight[aa] = 1/4;

(* weight[dd] = 1/2; *)
(* weight[gg] = 1/2; *)

(* d_comkdv.m *)