标题： 广义七阶KdV方程的守恒定律 显示英文标题

标题： Conservation laws for a generalized seventh order KdV equation

摘要： 在本文中，通过应用乘子方法，我们得到了一个依赖于七个任意非零参数的广义七阶KdV方程的低阶局部守恒定律的完整分类。 我们应用李方法，以任意参数为依据，对方程所接受的所有点对称性进行分类。 我们发现，除了可以通过观察得到的（标度对称性和空间与时间平移对称性）之外，没有参数的特殊情况下方程会接受额外的对称性。 我们考虑约化后的常微分方程，并从组合的$x$- 和$t$- 平移对称性中确定了约化方程的所有积分因子。 最后，我们观察到所有积分因子都是由广义七阶KdV方程的低阶乘子约化得到的。 显示英文摘要

摘要： In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined $x$- and $t$- translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation.