一维非局部Fisher-Kolmogorov-Petrovskii-Piskunov方程的准粒子
Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
AI总结：
本研究依托Maslov方法思想，用弱扩散近似下的半经典集中态方法构造非局部一维FKPP方程的类准粒子解，基于辅助ODE动力系统构建渐近展开并分析多种参数情形下的解，可用于预测种群格局动力学。
摘要：
我们采用弱扩散近似下的半经典集中态方法，构造了具有非局部非线性项的一维Fisher-Kolmogorov-Petrovskii-Piskunov（FKPP，费希尔-柯尔莫哥洛夫-彼得罗夫斯基-皮斯库诺夫）方程的类准粒子解。这类解可用于预测种群格局的动力学。准粒子的相互作用源于FKPP模型中的非局部竞争损耗。我们依托Maslov方法的思想发展了本研究方法的形式体系。原始非线性演化方程解的渐近展开构造，基于一个辅助常微分方程（ODEs）动力系统的解。我们在所提出方法的框架内，研究了对应于繁殖率和非局部竞争损耗的不同空间分布的多种特定情形下的渐近解。
英文摘要：
We construct quasiparticles-like solutions to the one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) with a nonlocal nonlinearity using the method of semiclassically concentrated states in the weak diffusion approximation. Such solutions are of use for predicting the dynamics of population patterns. The interaction of quasiparticles stems from nonlocal competitive losses in the FKPP model. We developed the formalism of our approach relying on ideas of the Maslov method. The construction of the asymptotic expansion of a solution to the original nonlinear evolution equation is based on solutions to an auxiliary dynamical system of ODEs. The asymptotic solutions for various specific cases corresponding to various spatial profiles of the reproduction rate and nonlocal competitive losses are studied within the framework of the approach proposed.
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