Arsie Alessandro, Lorenzoni Paolo, Moro Antonio
Department of Mathematics and Statistics , University of Toledo, 2801 W. Bancroft St. , Toledo, OH 43606, USA.
Dipartimento di Matematica e Applicazioni , Università di Milano-Bicocca , Via Roberto Cozzi 53, 20125 Milano, Italy.
Proc Math Phys Eng Sci. 2015 Jan 8;471(2173):20140124. doi: 10.1098/rspa.2014.0124.
We study normal forms of scalar integrable dispersive (not necessarily Hamiltonian) conservation laws, via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrized by infinitely many arbitrary functions that can be identified with the coefficients of the quasi-linear part of the equation. Moreover, in general, we conjecture that two scalar integrable evolutionary partial differential equations having the same quasi-linear part are Miura equivalent. This conjecture is also consistent with the tensorial behaviour of these coefficients under general Miura transformations.
我们通过杜布罗温 - 张微扰方案研究标量可积色散（不一定是哈密顿）守恒律的范式。我们的计算支持这样一个猜想：此类范式由无穷多个任意函数参数化，这些函数可与方程拟线性部分的系数等同。此外，一般来说，我们猜想具有相同拟线性部分的两个标量可积演化偏微分方程是三浦等价的。这个猜想也与这些系数在一般三浦变换下的张量行为一致。
