Short pulse equation: Nonlocal symmetries and applications
Abstract
We construct the nonlocal symmetries and Darboux transformation for the short pulse (SP) equation. The nonlocal symmetries of the SP equation can be obtained by the spectral gradient method. These nonlocal symmetries can then be localized by introducing suitable auxiliary variables, and the corresponding finite symmetry transformation for the enlarged system can be derived by solving the initial value problem. Moreover, we establish a connection between the nonlocal symmetries and Darboux transformation of the SP equation and those of the negative KdV equation. This connection allows us to construct n-fold Darboux transformations for the SP equation.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Nonlinear Photonic Systems
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Theoretical and Mathematical Physics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 228
- Issue
- 2
- Pages
- 1328–1340
- Publication date
- 1 August 2026
- Language
- EN