标题： 对扩散型霍林- Tanner 捕食者-猎物模型的对称性和精确解 显示英文标题

标题： Symmetries and exact solutions of the diffusive Holling-Tanner prey-predator model

摘要： 我们考虑在1D空间上通过引入扩散项扩展的经典Holling-Tanner模型。通过做出合理的简化，利用基于对称性的方法研究了扩散的Holling-Tanner系统。识别出Lie对称性和Q-条件（非经典）对称性。所得对称性用于寻找广泛范围的精确解，研究了它们的性质，并提出了可能的生物学解释。还绘制了最有趣的解的3D图。 显示英文摘要

摘要： We consider the classical Holling-Tanner model extended on 1D space by introducing the diffusion term. Making a reasonable simplification, the diffusive Holling-Tanner system is studied by means of symmetry based methods. Lie and Q-conditional (nonclassical) symmetries are identified. The symmetries obtained are applied for finding a wide range of exact solutions, their properties are studied and a possible biological interpretation is proposed. 3D plots of the most interesting solutions are drown as well.