− ∫ Γ$_{x}$ 2 sγϕ ( ∂$_{ν}$ψ ) ( |∇ $_{y}$z | 2 − |∇ $_{x}$z | 2 ) dS$_{x}$dydt + Γ$_{x}$ 2 s $^{3}$γ$^{3}$ϕ$^{3}$( ∂$_{ν}$ψ ) | z | 2 d$_{2}$ ( ψ ) dS$_{x}$dydt + ∫ Γ$_{x}$ 2 s ( γϕd$_{1}$ ( ψ ) + γ $^{2}$ϕd$_{2}$ ( ψ ) z ( ∂$_{ν}$z ) dS$_{x}$dydt − Γ$_{x}$ s (( γ $^{2}$ϕd$_{1}$ ( ψ ) + γ $^{3}$ϕd$_{2}$ ( ψ ) ( ∂$_{ν}$ψ ) + γ $^{2}$ϕ∂$_{ν}$ ( d$_{2}$ ( ψ )) ) | z | 2 dS$_{x}$dydt. (3.28) 2 Re ( P + s z, P − s z ) L $^{2}$(Ω) = m ∑ i,j =1 Re ∫ Ω 4 sγϕψ$_{y}$$_{i}$$_{y}$$_{j}$ z$_{y}$$_{j}$ z$_{y}$$_{i}$dxdydt + n i,j =1 Re ∫ Ω 4 sγϕψ$_{x}$$_{i}$$_{x}$$_{j}$z$_{x}$$_{i}$z$_{x}$$_{j}$dxdydt + ∫ Ω 4 sγ $^{2}$ϕ |∇ $_{y}$ψ · ∇ $_{y}$z − ∇ $_{x}$ψ · ∇ $_{x}$z | 2 dxdydt + Ω 4 s $^{3}$γ$^{4}$ϕ3 | z | $^{2}$( d$_{2}$ ( ψ )) 2 dxdydt + B$_{0}$ + X$_{1}$ + X$_{2}$, X$_{1}$ = ∫ Ω 2 s $^{3}$γ$^{3}$ϕ3 | z | 2 d$_{5}$ ( ψ ) dxdydt, X$_{2}$ = − 2 Im ∫ Ω s ( − 2 γ $^{2}$βt ) zϕ ∇ $_{y}$ψ · ∇ $_{y}$zdxdydt +2 Im Ω s − 2 γ $^{2}$βt zϕ ∇ $_{x}$ψ · ∇ $_{x}$zdxdydt − ∫ Ω sγ $^{4}$ϕ | z | $^{2}$( d$_{2}$ ( ψ )) 2 dxdydt − Ω sγ $^{2}$ϕ | z | 2 d$_{3}$ ( ψ ) dxdydt − ∫ Ω sγ $^{3}$ϕ | z | 2 d$_{4}$ ( ψ ) dxdydt, where Then from (3.22)-(3.28) we can write 16