gMuNuGeneric={{-f[x], 0 ,0,0}, {0, 1/f[x], 0, 0}, {0, 0, C[x]^2, 0}, {0, 0, 0,C[x]^2}};
MatrixForm[gMuNuGeneric];
GMuNuGeneric=Inverse[gMuNuGeneric];
coord2D={t, x, y, z};
sqrtngGeneric=Simplify[Sqrt[-Det[gMuNuGeneric]], {C[x]>0}];
box4DGeneric=0;box4D2Generic=0;
Do[ {box4D2Generic=1/sqrtngGeneric*(D[sqrtngGeneric*GMuNuGeneric[[i,j]]*D[Theta[t,x]/C[x],coord2D[[j]]] ,coord2D[[i]]]),box4DGeneric=box4DGeneric+box4D2Generic}, {i, 1, 2}, {j, 1, 2}];
box4DGenericDimple=Collect[Simplify[box4DGeneric], {Derivative[0,1][Theta][t,x], Derivative[2,0][Theta][t,x], Derivative[0,2][Theta][t,x],Theta[t,x]}];
box4DGenericDimpleCorrected=Simplify[box4DGenericDimple*C[x]];

The Potential contains already contains an overall negative sign because it is found through the Mode equation.

PotentialGeneric=Coefficient[box4DGenericDimpleCorrected,Theta[t,x]];
EffectivePotentialGeneric=PotentialGeneric*f[x];
A2[x_]=n[x]*(c[x]^2-v[x]^2)/c[x];
DA2[x_]=D[A2[x], x];
B2[x_]=(Sqrt[n[x]/c[x]]);
DB2[x_]=D[B2[x], x];
DDB2[x_]=D[DB2[x], x];
EffectivePotentialGeneric2019=Expand[(EffectivePotentialGeneric/.{f[x]->A2[x], f'[x]->DA2[x], C[x]->B2[x],C'[x]->DB2[x] ,C''[x]->DDB2[x] })];

rho1plus=264/100;
rho1minus=11;
XXX=27/10*10^(-7);
TTT=10^(-4);
Mplus=rho1minus/rho1plus;
uNISt=166053906660/100000000000*10^-27;(*1.66053906660*10^-27*);
hbarNIST=1054571817/1000000000*10^-34;(*1.054571817*10^-34*);
MRB87NISt=86909187/1000000*uNISt;(*86.909187*uNISt*);
CInt2016=25*10^-5;
CExt2016=57*10^-5;
XiInt=hbarNIST/(MRB87NISt*CInt2016);
XiExt=hbarNIST/(MRB87NISt*CExt2016);
Xi=Sqrt[XiInt*XiExt]
sigma=Sqrt[Mplus-1]/(Xi);
nZero[x1_]=(1/XXX)*rho1plus*(Mplus+(1-Mplus)/(Cosh[sigma*(xstart1)]^2));
vZero=1/(TTT*nZero[xstart1]);
cZero=(XXX/TTT)*Sqrt[(XXX*nZero[xstart1])/(rho1plus*rho1minus^2)];

N[Xi]

ncvPlot6=Plot[{ nZero[xstart1]*XXX*TTT, cZero, vZero}, {xstart1, -2*Xi, Xi}, PlotLegends->{ "n[x]*X*T","c[x]", "v[x]"}, ImageSize->Large]

ncvPlot5=Plot[{ cZero, vZero}, {xstart1, 9.616971*10^-7, 9.616973*10^-7}, PlotLegends->{"c[x]", "v[x]"}, ImageSize->Large]

xstartSolver={xstart1-> 9.616971*10^-7};

N[9616971/10000000000000]

leftstop=-9616971/10000000000000;

n2[x_]=(1/XXX)*rho1plus*(Mplus+(1-Mplus)/(Cosh[sigma*(x+9616971/10000000000000)]^2));(*This contains approximately the location of c[x]=v[x]*)
dn2=D[n2[x], x]/n2[x];
ddn2=D[dn2, x]/n2[x];
v2=1/(TTT*n2[x]);
dv2=D[v2, x]/n2[x];
ddv2=D[dv2, x]/n2[x];
c2=(XXX/TTT)*Sqrt[(XXX*n2[x])/(rho1plus*rho1minus^2)];
dc2=D[c2, x]/n2[x];
ddc2=D[dc2,x]/n2[x];
N[(c2-v2)/.x->+Xi];

Thcalc1=N[(2*N[v2/.x->0, 20]*Sqrt[N[c2/.x->-1000*Xi, 20]*N[v2/.x->-1000*Xi, 20]])/((N[c2/.x->-1000*Xi, 20]*N[v2/.x->-1000*Xi, 20])+N[v2/.x->0]^2),20]

ncvPlot4=Plot[{ n2[x]*XXX*TTT, c2, v2}, {x, leftstop, 2*Xi}, PlotLegends->{ "n(x) X T","c(x)", "v[x]"}, ImageSize->Large]

n3=HeavisideTheta[x-leftstop]n2[x]+HeavisideTheta[leftstop-x]n2[leftstop];
c3=HeavisideTheta[x-leftstop]c2+HeavisideTheta[leftstop-x](c2/.{x-> leftstop});
v3=HeavisideTheta[x-leftstop]v2+HeavisideTheta[leftstop-x](v2/.{x-> leftstop});

ncvPlot=Plot[{ n3*XXX*TTT, c3, v3}, {x, -2*Xi, 2*Xi}, PlotLegends->{ Style["n(x)TX", 14],Style["c(x)", 14], Style["|v(x)|", 14]},  ImageSize-> Full,PlotStyle->{{Blue, Thick},{Orange, Thick, Dashed}, {Green,Thick,  Dotted}  },FrameLabel->{Style[ x, 14],None  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Table[{(2*k+1)*10^(-4),(2*k+1)* Superscript["x 10",-6]},{k,1,4}], None},{ Table[{2*k*10^(-6),2*k*Superscript["x 10",-6]},{k,-4,4}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/ncvPlot.pdf",ncvPlot, ImageResolution->200]

Rhcalc1=N[(N[v2/.x->-1000*Xi, 20]*N[c2/.x->-1000*Xi, 20]-N[v2/.x->-0, 20]^2)/(N[v2/.x->-1000*Xi, 20]*N[c2/.x->-1000*Xi, 20]+N[v2/.x->-0, 20]^2),20]

N[(c2-v2)/.x->0]

(*NSolve[v2==c2, x, Reals]*)

ncvPlot3=Plot[{ n2[x]*XXX*TTT, c2, v2}, {x, -2*Xi, 0}, PlotLegends->{ "n[x]*X*T","c[x]", "v[x]"}, ImageSize->Large]

(*Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\CorrectCVN\\2020Files\\Plots\\ncvPlot.jpg",ncvPlot, ImageResolution->200]*)

EffectivePotential2019Genericv1Values=HeavisideTheta[x-leftstop]*EffectivePotentialGeneric2019/.{c[x]->c2, v[x]->v2,n[x]->n2[x],v'[x]->dv2,c'[x]->dc2,n'[x]->dn2,c''[x]->ddc2, v''[x]->ddv2  ,  n''[x]->ddn2};
EffectivePotential2019PlotExterior=Plot[-EffectivePotential2019Genericv1Values, {x, 0, 2*Xi},PlotRange->All,Exclusions->None, WorkingPrecision->30,ImageSize-> Full,PlotStyle->{{Blue, Thickness[0.001]}},FrameLabel->{Style[ x, 14],Style[ Subscript["V","eff"], 14]  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{ Table[{3*k*10^(3),3*k Superscript["x 10",3]},{k,-3,3}] ,None},{{{0,0},{(1/1000000),(Superscript["10", -6])},{(1/500000),2 (Superscript["x10", -6])},{(3/1000000),3 (Superscript["x10", -6])}}, None}},Frame->True, AspectRatio->2/3]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17EffectivePotential2019PlotExterior.pdf",EffectivePotential2019PlotExterior, ImageResolution->200]

EffectivePotential2019PlotInterior=Plot[-EffectivePotential2019Genericv1Values, {x, -2*Xi, 0},PlotRange->All,Exclusions->None, WorkingPrecision->30,ImageSize-> Full,PlotStyle->{{Blue, Thickness[0.001]}},FrameLabel->{Style[ x, 14],Style[ Subscript["V","eff"], 14]  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{ Table[{2*k*10^(7),2*k *Superscript["x10",7]},{k,0,3}] ,None},{{{-(3/1000000),-3 (Superscript["x10", -6])},{-(1/500000),-2 (Superscript["x10", -6])},{-(1/1000000),-(Superscript["10", -6])},{0,0}}, None}},Frame->True, AspectRatio->2/3]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17EffectivePotential2019PlotInterior.pdf",EffectivePotential2019PlotInterior, ImageResolution->200]

Table[{3*k*10^(3),3*k Superscript["x 10",3]},{k,-3,3}]

{{-9000,-9 (Superscript["x 10", 3])},{-6000,-6 (Superscript["x 10", 3])},{-3000,-3 (Superscript["x 10", 3])},{0,0},{3000,3 (Superscript["x 10", 3])},{6000,6 (Superscript["x 10", 3])},{9000,9 (Superscript["x 10", 3])}}

Table[{k*10^(-6),k Superscript["x10",-6]},{k,0,3}]

{{0,0},{(1/1000000),(Superscript["10", -6])},{(1/500000),2 (Superscript["x10", -6])},{(3/1000000),3 (Superscript["x10", -6])}}

{{0,0},{(1/1000000),(Superscript["10", -6])},{(1/500000),2 (Superscript["x10", -6])},{(3/1000000),3 (Superscript["x10", -6])}}

Table[{k*10^(-6),k Superscript["x10",-6]},{k,-3, 0}]

{{-(3/1000000),-3 (Superscript["x10", -6])},{-(1/500000),-2 (Superscript["x10", -6])},{-(1/1000000),-(Superscript["10", -6])},{0,0}}