Drinfeld–Sokolov–Wilson equation

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:[1]

∂ 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\\[5pt]&{\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

  1. ^ Weisstein, Eric W. "Drinfeld–Sokolov–Wilson Equation". MathWorld.


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