Abstract. We present a new Riemann-Hilbert problem formalism for the initial value problem for the derivative nonlinear Schrödinger (DNLS) equation:

In engineering design, capturing customers' requirements exactly and transforming them into design specifications are vital to designing a quality product. However, the expressions of customer requirements are normally imprecise and ambiguous due to their linguistic origins. There is still a lack of a systematic approach for elaborating these requirements and transforming them from informal to formal. Therefore, this article provides a scenario-based, systematic approach for requirements management in engineering design. The requirements management process is conceptualized as a three-phase model, and scenarios are integrated into this model for elaborating and formally representing the requirements. A case study of a soy milk maker design is also provided to demonstrate the proposed approach.

We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrödinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed: (i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; (ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; (iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.