论文标题
扩散的Lotka-Volterra系统的确切解决方案的构建和应用：审查和新结果
Construction and application of exact solutions of the diffusive Lotka-Volterra system: a review and new results
论文作者
论文摘要
这篇综述总结了所有已知结果（直到这个日期），内容涉及具有扩散的经典Lotka-volterra系统的整合方法，并提出了广泛的精确解决方案，从适用性角度来看，这是最重要的。这是朝这个方向上的第一次尝试。由于扩散的Lotka-volterra系统用于数学建模，在生态学，生物学，医学，物理和化学方面进行了各种各样的过程，因此该评论不仅对来自应用数学的专家，而且对于其他科学分支的专家来说都应该很有趣。获得的精确解决方案也可以用作测试问题，以估算解决相关边界价值问题的近似分析和数值方法的准确性。
This review summarizes all known results (up to this date) about methods of integration of the classical Lotka-Volterra systems with diffusion and presents a wide range of exact solutions, which are the most important from applicability point of view. It is the first attempt in this direction. Because the diffusive Lotka-Volterra systems are used for mathematical modeling enormous variety of processes in ecology, biology, medicine, physics and chemistry, the review should be interesting not only for specialists from Applied Mathematics but also those from other branches of Science. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.
