A Bäcklund transformation (BT), which involves both independent and dependent variables, is established and studied for the short pulse (SP) equation. Based it, the nonlinear superposition formulae for 2‐, 3‐, and 4‐BT are presented. The general result for the composition of ‐BTs is achieved and given in terms of determinants. As applications, various solutions including loop solitons, breather solutions, and their interaction solutions are worked out.

中文翻译：

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短脉冲方程：Bäcklund变换和应用

建立了涉及独立变量和因变量的Bäcklund变换（BT），并研究了短脉冲（SP）方程。在此基础上，给出了2-BT，3-BT和4-BT的非线性叠加公式。BT组成的总体结果已经实现，并根据决定因素给出。作为应用，制定了各种解决方案，包括回路孤子，通气解决方案及其交互解决方案。