In[]:=
eq0=D[u[x,t],{t,2}]-(v-2)*u[x,t]-(v+v1/μ)*(-u[x,t]^3+u[x,t]^5);​​eq0/.uFunction[{x,t},U[Sqrt[k](x-ct)]]​​%/.Sqrt[k](x-ct)ξ​​%/.{UFunction[ξ,Sqrt[W[ξ]]]}//Simplify​​Collect[%*4μW[ξ]^(3/2)/(4c^2μW[ξ]),{W'[ξ],W''[ξ]}]
Out[]=
-(-2+v)U
k
(-ct+x)-v+
v1
μ
-
3
U
k
(-ct+x)
+
5
U
k
(-ct+x)
+
2
c
k
′′
U

k
(-ct+x)
Out[]=
-(-2+v)U[ξ]-v+
v1
μ
(-
3
U[ξ]
+
5
U[ξ]
)+
2
c
k
′′
U
[ξ]
Out[]=
-4(-2+v)μ
2
W[ξ]
+4(v1+vμ)
3
W[ξ]
-4(v1+vμ)
4
W[ξ]
-
2
c
kμ
2
′
W
[ξ]
+2
2
c
kμW[ξ]
′′
W
[ξ]
4μ
3/2
W[ξ]
Out[]=
-4(-2+v)μ
2
W[ξ]
+4(v1+vμ)
3
W[ξ]
-4(v1+vμ)
4
W[ξ]
4
2
c
μW[ξ]
-
k
2
′
W
[ξ]
4W[ξ]
+
1
2
k
′′
W
[ξ]