School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather and rogue wave solutions to the CCSP equation. In case of vanishing boundary condition (VBC), we perform the inverse scattering analysis to understand the soliton solution better. Breather and rogue wave solutions are constructed in case of non-vanishing boundary condition (NVBC). Moreover, we conduct a modulational instability (MI) analysis based on the method of squared eigenfunctions, whose result confirms the condition for the existence of rogue wave solution.
Feng, Bao-Feng, and Liming Ling. "Darboux transformation and solitonic solution to the coupled complex short pulse equation." Physica D: Nonlinear Phenomena 437 (2022): 133332. https://doi.org/10.1016/j.physd.2022.133332
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Physica D: Nonlinear Phenomena
Original published version available at https://doi.org/10.1016/j.physd.2022.133332