ABSTRACT
Let us expand (43.1.1.1) in powers of the small parameter a in a neighborhood of a0, taking into account (43.1.1.2), and then divide the resulting equation by a – a0 and pass to the limit for a→ a0. As a result, we obtain a first-order linear partial differential equation for the function w:
ϕ◦a(x, t) ∂w
∂x + ψ◦a(x, t)
∂w
∂t + θ◦a(x, t)w = 0, (43.1.1.3)
where we have used the following notation:
ϕ◦a(x, t) = ∂ϕ
∂a
∣∣∣ a=a0
, ψ◦a(x, t) = ∂ψ
∂a
∣∣∣ a=a0
, θ◦a(x, t) = ∂θ
∂a
∣∣∣ a=a0
.
