标题： 色散less Benney和Toda层次的代数和Hamilton结构 显示英文标题

标题： The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies

摘要： 多分量色散less Benny和Toda层次的代数和Hamilton结构被研究。 这是通过使用一组修改后的变量实现的，在这组变量中基本场之间存在对称性。 这种对称性使得通常以残差形式隐式给出的公式，如守恒荷和通量，可以显式计算。 作为这些结果的一个推论，建立了Benny和Toda层次之间的等价性。 进一步表明，此类数量可以用广义超几何函数表示，最简单的例子涉及Legendre多项式。 然后将这些结果推广到由有理Lax函数和对数函数导出的系统。 还研究了各种约化。 显示英文摘要

摘要： The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields. This symmetry enables formulae normally given implicitly in terms of residues, such as conserved charges and fluxes, to be calculated explicitly. As a corollary of these results the equivalence of the Benney and Toda hierarchies is established. It is further shown that such quantities may be expressed in terms of generalized hypergeometric functions, the simplest example involving Legendre polynomials. These results are then extended to systems derived from a rational Lax function and a logarithmic function. Various reductions are also studied.