In[]:=
func1[x_,t_]=With[{ξ=γ*x+ω*t,θ=η*x+σ*t},W[ξ]E^(Iθ)]​​pde=I*(D[w[x,t],t]+D[w[x,t],{x,3}]+
ρ
1
*D[w[x,t],x]*
2
Abs[w[x,t]]
)+
2
Abs[w[x,t]]
*(
ρ
2
*w[x,t])+I*
ρ
3
*D[
2
Abs[w[x,t]]
,x]*w[x,t]0;​​​​ss=Assuming[{{x,t,γ,ω,η,σ}∈Reals},pde/.wfunc1//Simplify]/.γ*x+ω*tξ
Out[]=
(xη+tσ)

W[xγ+tω]
Out[]=
W[ξ]
3
η
-σ+
2
Abs[W[ξ]]
(-η
ρ
1
+
ρ
2
)+2
(xη+tσ)

γAbs[W[ξ]]
ρ
3
′
Abs

(xη+tσ)

W[ξ]
′
W
[ξ]+(-3γ
2
η
+ω+γ
2
Abs[W[ξ]]
ρ
1
)
′
W
[ξ]+
2
γ
3η
′′
W
[ξ]+γ
(3)
W
[ξ]2
(xη+tσ)

ηAbs[W[ξ]]
ρ
3
2
W[ξ]
′
Abs

(xη+tσ)

W[ξ]
W[ξ]
3
η
-σ+
2
Abs[W[ξ]]
(-η
ρ
1
+
ρ
2
)+2
(xη+tσ)

γAbs[W[ξ]]
ρ
3
′
Abs
[
(xη+tσ)

W[ξ]]
′
W
[ξ]+(-3γ
2
η
+ω+γ
2
Abs[W[ξ]]
ρ
1
)
′
W
[ξ]+
2
γ
3η
′′
W
[ξ]+γ
(3)
W
[ξ]2
(xη+tσ)

ηAbs[W[ξ]]
ρ
3
2
W[ξ]
′
Abs
[
(xη+tσ)

W[ξ]]​​
​​​​(*w(x,t)=u(x,t),p1=ν,p2=a,p3=k*)​​​​
In[]:=
func[x_,y_,t_]=With[{ξ=x+y+αt,θ=αx+βy+γt},U[ξ]E^(Iθ)]​​pde=I*D[u[x,y,t],t]-1/2D[u[x,y,t],{x,2}]-(Abs[u[x,y,t]]^2-A)*u[x,y,t]0;​​​​Assuming[{{x,y,t,α,β,γ}∈Reals},pde/.ufunc//Simplify]/.x+y+αtξ
Out[]=
(xα+yβ+tγ)

U[x+y+tα]
Out[]=
(2A+
2
α
-2γ-2
2
Abs[U[ξ]]
)U[ξ]
′′
U
[ξ]