用合偶守恒律积分线性偏微分方程组
The integration of systems of linear PDEs using conservation laws of syzygies
摘要：
提出了一种新的线性偏微分方程（PDE）的积分方法，使合轨线能满足守恒律。这些合点是作为微分Groebner基计算的副产品免费提供的。与积分单个方程并将结果代入其他方程的更明显的方法相比，新技术一次积分多个方程，因此引入了暂时更少的新积分函数，并且还依赖于更少的变量。特别是对于多变量高阶偏微分方程系统，传统的积分方法可能会导致积分函数数目的爆炸，而新的方法避免了这一问题。另一个好处是，解决方案中的冗余自由函数被防止或至少减少了它们的数量。
英文摘要：
A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Groebner Basis computation. Compared with the more obvious way of integrating a single equation and substituting the result in other equations the new technique integrates more than one equation at once and therefore introduces temporarily fewer new functions of integration that in addition depend on fewer variables. Especially for high order PDE systems in many variables the conventional integration technique may lead to an explosion of the number of functions of integration which is avoided with the new method. A further benefit is that redundant free functions in the solution are either prevented or that their number is at least reduced.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
