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Past exam of the mathematics course of the University of Cambridge
/
2024
/
ii
/
Paper 2
/
34C
/
a
/
Solution
...
Past exam of the mathematics course of the University of Cambridge
2024
ii
Paper 2
34C
a
OurBigBook.com
Words: 37
The stated operators form a
Lax pair
when the KdV equation is equivalent to
∂
t
L
=
[
L
,
A
]
=
L
A
−
A
L
.
(233)
Indeed, if
L
ϕ
=
k
2
ϕ
,
differentiation
and this identity show
(
L
−
k
2
)
(
A
ϕ
+
∂
t
ϕ
)
=
([
L
,
A
]
−
L
t
)
ϕ
=
0.
(234)
Thus
∂
t
+
A
preserves every spectral eigenspace, which is the
isospectral Lax equation
formulation.
Solved by gpt-5.6-sol high.
Ancestors
(11)
A
34C
Paper 2
Ii
2024
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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