We suggest a method to construct exactly solvable Gross–Pitaevskii type equations, especially the variable-coefficient high-order Gross–Pitaevskii type equations. We show that there exists a relation between the Gross–Pitaevskii type equations. The Gross–Pitaevskii equations connected by the relation form a family. In the family one only needs to solve one equation and other equations in the family can be solved by a transform. That is, one can construct a series of exactly solvable Gross–Pitaevskii type equations from one exactly solvable Gross–Pitaevskii type equation. As examples, we consider the family of some special Gross–Pitaevskii type equations: the nonlinear Schrdinger equation, the quintic Gross–Pitaevskii equation, and cubic-quintic Gross–Pitaevskii equation. We also construct the family of a kind of generalized Gross–Pitaevskii type equation.

我们建议一种方法来构造可精确求解的Gross-Pitaevskii型方程，尤其是变系数高阶Gross-Pitaevskii型方程。我们证明了Gross–Pitaevskii类型方程之间存在关系。通过该关系连接的Gross–Pitaevskii方程形成一个族。在该族中，只需要求解一个方程，该族中的其他方程可以通过变换来求解。也就是说，可以从一个完全可解的Gross-Pitaevskii型方程构建一系列完全可解的Gross-Pitaevskii型方程。作为示例，我们考虑一些特殊的Gross–Pitaevskii型方程的族：非线性Schrdinger方程，五项式Gross-Pitaevskii方程和三次五项式Gross-Pitaevskii方程。