This presentation I made in order to present and explain my project thesis in my undergraduate study.

6. DERIVATION OF NLS EQUATION:
NLS equation can be derive using following steps
1. Maxwell’s Equation with nonlinear polarization term.
• ∇×E = ∂B/ ∂t,
• ∇×H = J +∂D/ ∂t,
• ∇·D = ρ,
• ∇·B = 0,
where
D = 𝜀0E +P, and B = 𝜇0H + M.
2. Using these equations, nonlinear Maxwell equation can be found which
is
• ∇2E – (1/ c2)(∂2E/ ∂2t) = µ0(∂2P/ ∂t2), (a)
Here P(r,t)=PL(r,t)+PNL(r,t).
• ∇2E- (1 /c2)(∂2E/ ∂t2) = µ0(∂2PL/ ∂t2) +µ0(∂2PNL/ ∂t2), (b)