论文信息 - The Short Pulse Equation Is Integrable

The Short Pulse Equation Is Integrable

We prove that the Schafer–Wayne short pulse equation (SPE), which describes the propagation of ultrashort optical pulses in nonlinear media, is integrable. First, we discover a Lax pair of the SPE that is found to be of the Wadati–Konno–Ichikawa type. Second, we construct a chain of transformations that relates the SPE with the sine-Gordon equation.

Sergei Sakovich | Anton Sakovich

[1] Christopher K. R. T. Jones,et al. Ultra-short pulses in linear and nonlinear media , 2004, nlin/0408020.

[2] P. Olver. Applications of Lie Groups to Differential Equations , 1986 .

[3] S. Yu. Sakovich. Cyclic Bases of Zero-Curvature Representations: Five Illustrations to One Concept , 2002, nlin/0212019.

[4] Kiyoshi Sogo,et al. GAUGE TRANSFORMATIONS IN SOLITON THEORY , 1983 .

[5] S. Yu. Sakovich. On integrability of one third-order nonlinear evolution equation , 2003 .

[6] M. Boiti,et al. The Nonlinear Evolution Equations Related to the Wadati-Konno-Ichikawa Spectral Problem , 1983 .

[7] T. Schäfer,et al. Propagation of ultra-short optical pulses in nonlinear media , 2022 .

[8] Kimiaki Konno,et al. New Integrable Nonlinear Evolution Equations , 1979 .

[9] C. E. Wayne,et al. Propagation of ultra-short optical pulses in cubic nonlinear media , 2004 .

[10] S. Sakovich. Fujimoto-Watanabe equations and differential substitutions , 1991 .

[11] Y. Ishimori. A Relationship between the Ablowitz-Kaup-Newell-Segur and Wadati-Konno-Ichikawa Schemes of the Inverse Scattering Method , 1982 .

[12] Mark J. Ablowitz,et al. Solitons and the Inverse Scattering Transform , 1981 .