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Arnold's Trivium
1991 Arnold's Trivium
83
Problem 83
Problem 83
Source:
July 1, 2010
Problem Statement
Find solutions of the equation
u
t
=
u
x
x
x
+
u
u
x
u_t=u_{xxx}+uu_x
u
t
=
u
xxx
+
u
u
x
in the form of a traveling wave
u
=
φ
(
x
−
c
t
)
u=\varphi(x-ct)
u
=
φ
(
x
−
c
t
)
,
φ
(
±
∞
)
=
0
\varphi(\pm\infty)=0
φ
(
±
∞
)
=
0
.
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