论文标题
确切可解决的GROSS-PITAEVSKII类型方程
Exactly solvable Gross-Pitaevskii type equations
论文作者
论文摘要
TWE提出了一种构建准确可溶解的Gross-Pitaevskii类型方程的方法，尤其是可变的高阶高阶毛taevskii类型方程。我们表明，Gross-Pitaevskii类型方程之间存在关系。由关系形成一个家庭的关系的毛taevskii方程。在家庭中，只需要解决一个方程式，而家庭中的其他方程可以通过转换来解决。也就是说，一个人可以从一个准确可解决的gross-pitaevskii类型方程中构造一系列可解决的gross-pitaevskii类型方程。作为示例，我们考虑了一些特殊的毛皮pitaevskii类型方程的家族：非线性schrödinger方程，Quintic Gross-pitaevskii方程和立方Quintic Gross-Pitaevskii方程。我们还构建了一种普遍的毛皮pitaevskii型方程的家族。
TWe 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 Schrödinger 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.
