Korteweg-de Vries (KdV)-type models are frequently seen during the investigations on the optical fibers, cosmic plasmas, planetary oceans and atmospheres. In this paper, for an extended three-coupled KdV system, noncharacteristic movable singular manifold and symbolic computation help us bring about four sets of the auto-Bäcklund transformations with some solitons. All of our results rely on the coefficients in that system.

中文翻译：

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扩展三耦合 Korteweg-de Vries 系统的奇异流形、自动 Bäcklund 变换和带孤子的符号计算步骤

Korteweg-de Vries (KdV) 型模型在光纤、宇宙等离子体、行星海洋和大气的研究中经常出现。在本文中，对于扩展的三耦合 KdV 系统，非特征可移动奇异流形和符号计算帮助我们实现了四组带有一些孤子的自 Bäcklund 变换。我们所有的结果都依赖于该系统中的系数。