标题： 施盖达-川崎-寺田模型：条件对称性、精确解及其性质 显示英文标题

标题： The Shigesada-Kawasaki-Teramoto model: conditional symmetries, exact solutions and their properties

摘要： 我们研究了一个著名的Shigesada-Kawasaki-Teramoto模型的简化形式，该模型由两个具有交叉扩散的非线性反应-扩散方程组成。 使用一种用于构建条件对称性的算法，得到了一组完整的Q-条件（非经典）对称性。 所获得的对称性被用于寻找广泛范围的精确解，其中一些解可能的生物学解释也被提出。 此外，还提出了简化模型在聚合过程中的另一种应用，并在此情况下也找到了精确解。 显示英文摘要

摘要： We study a simplification of the well-known Shigesada-Kawasaki-Teramoto model, which consists of two nonlinear reaction-diffusion equations with cross-diffusion. A complete set of Q-conditional (nonclassical) symmetries is derived using an algorithm adopted for the construction of conditional symmetries. The symmetries obtained are applied for finding a wide range of exact solutions, possible biological interpretation of some of which being presented. Moreover, an alternative application of the simplified model related to the polymerisation process is suggested and exact solutions are found in this case as well.