The Drinfeld–Sokolov–Wilson (DSW) equations are an integrable system of two coupled nonlinear partial differential equations proposed by Vladimir Drinfeld and Vladimir Sokolov, and independently by George Wilson:
∂
u
∂
t
+
3
v
∂
v
∂
x
=
0
∂
v
∂
t
=
2
∂
3
v
∂
x
3
+
∂
u
∂
x
v
+
2
u
∂
v
∂
x
{\displaystyle {\begin{aligned}&{\frac {\partial u}{\partial t}}+3v{\frac {\partial v}{\partial x}}=0\\&{\frac {\partial v}{\partial t}}=2{\frac {\partial ^{3}v}{\partial x^{3}}}+{\frac {\partial u}{\partial x}}v+2u{\frac {\partial v}{\partial x}}\end{aligned}}}
References
Weisstein, Eric W. "Drinfeld–Sokolov–Wilson Equation" . MathWorld .
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