一维抛物-抛物Patlak-Keller-Segel趋化模型：特殊可积情形和孤子解
The 1D parabolic-parabolic Patlak-Keller-Segel model of chemotaxis: the particular integrable case and soliton solution
摘要：
本文研究了一维抛物-抛物Patlak-Keller-Segel趋化模型。对于化学物质的扩散系数等于2的情况，约化的系统在行波变量方面似乎是可积的，并且允许解析解。我们得到了精确的孤子解，其中之一就是Korteweg-de Vries方程的单孤子解。
英文摘要：
In this paper we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears integrable and allows the analytical solution. We obtain the exact soliton solutions, one of which is exactly the one-soliton solution of the Korteweg-de Vries equation.
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