The exact solution is obtained for a class of nonlinear Langevin equations, driven by Gaussian white noise, with drift and diffusion coefficients separable in time and space. In addition, the solutions for particular cases of the drift and diffusion coefficients have also been recovered and compared; it is shown that these systems can share similar solutions for specific ranges of the time-dependent drift and diffusion coefficients. The application of the system to population growth models is also discussed.

中文翻译：

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漂移和扩散系数在时间和空间上可分离的非线性Langevin方程的相似解

对于一类由高斯白噪声驱动的非线性Langevin方程，可以得到精确的解，其漂移和扩散系数在时间和空间上是可分离的。另外，还针对特定情况下的漂移和扩散系数的解决方案进行了比较。结果表明，对于时间相关的漂移和扩散系数的特定范围，这些系统可以共享相似的解决方案。还讨论了该系统在人口增长模型中的应用。