无色散Hirota型可积方程与Lagrange Grassmannian超曲面
Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian
摘要：
研究了F（u_{xx}，u_{xy}，u_{yy}，u_{xt}，u_{yt}，u_{tt}）=0的二阶可积方程.常见的例子包括Boyer-Finley方程、无色散Kadomtsev-Petviashvili方程的势形式、无色散Hirota方程等。我们证明了问题的自然等价群同构于Sp（6），揭示了上述类型的微分方程与Lagrangian Grassmannian超曲面之间的显著对应。证明了无色散Hirota型可积方程的模空间是21维的，等价群Sp（6）在模空间上的作用有开轨.
英文摘要：
We investigate integrable second order equations of the form F(u_{xx}, u_{xy}, u_{yy}, u_{xt}, u_{yt}, u_{tt})=0. Familiar examples include the Boyer-Finley equation, the potential form of the dispersionless Kadomtsev-Petviashvili equation, the dispersionless Hirota equation, etc. The integrability is understood as the existence of infinitely many hydrodynamic reductions. We demonstrate that the natural equivalence group of the problem is isomorphic to Sp(6), revealing a remarkable correspondence between differential equations of the above type and hypersurfaces of the Lagrangian Grassmannian. We prove that the moduli space of integrable equations of the dispersionless Hirota type is 21-dimensional, and the action of the equivalence group Sp(6) on the moduli space has an open orbit.
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