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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher–Kolmogorov–Petrovskii– Piskunov equation
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Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher–Kolmogorov–Petrovskii– Piskunov equation

机译：非局部Fisher–Kolmogorov–Petrovskii–Piskunov方程在低维流形上的半经典有限分布形式的模式形成

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摘要

We have investigated the pattern formation in systems described by the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables. We have obtained a system of integro-differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions. Also, asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasisteady- state pattern on the concentration manifold. The approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations.
机译：我们已经研究了非局部Fisher-Kolmogorov-Petrovskii-Piskunov方程描述的系统中的模式形成，其中模式浓度域的维数小于自变量域的维数。我们已经获得了一个积分微分方程系统，该积分微分方程系统描述了轨迹集中函数类别中某个模式的浓度域动态和半经典有限密度分布。此外，已获得渐近的长时间解，该解描述了浓度歧管上的准稳态模式的半经典有限分布。通过实例说明了该方法，该方法的解析解与数值计算的结果非常吻合。

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