Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems

我们提出了任意微分方程的修正形式拉格朗日结构，并将其应用于利用Noether定理推导守恒律。这也被用来构造非变分方程组的(形式)变分积分器。我们还利用Hirota的双线性方法和对称性分析方法分析了变系数KdV系统的新的波结构，得到了各种孤子以及新的三阶Painleve方程。

We proposed the modified formal Lagrangian structure for arbitrary differential equations and applied it to the derivation of conservation laws using Noether’s theorem. This is also used to constructing (formal) variational integrator for nonvariational equations. We also analyzed novel wave structures of a variable-coefficient KdV system by Hirota’s bilinear method and symmetry analysis; a variety of solitons were obtained as well as novel third-order Painleve equations.