Bäcklund transformations are applied to study the Gross–Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwarzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross–Pitaevskii equation are obtained.

中文翻译：

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Gross-Pitaevskii方程：Bäcklund变换和公认的解

Bäcklund变换用于研究Gross-Pitaevskii方程。得到先前结果的支持，构造了该方程式所接受的一类Bäcklund变换。Schwarzian导数及其不变性证明是本研究的关键工具。获得了Gross – Pitaevskii方程的示例和显式解。