Today, engineers face an increasing challenge in advanced engineering applications that are based on efficient mathematical models for propagation and transition phenomena. Propagation aspects implying commutative and/or additive consequences of quantum physics are used extensively in the design of Long Range Transmission Systems. Differential geometry is adapted for solving nonlinear partial differential equations with very great number of variables for transitions in Complex Optoelectronics Systems. Special Mathematical Functions are used in modeling very small-scale material properties (energy levels and induced transitions) in quantum physics for the design of nanostructures in microelectronics. Time series with extremely high transmission rates are used for Multiplexed Transmission Systems for large communities. All these advanced engineering subjects require Efficient Mathematical Models in the development of classical tools for Complex Systems such as differential geometry, vector algebra, partial differential equations, and time series dynamics. The objective in such applications is to take into consideration efficiency aspects of mathematical and physical models required by Basic Phenomena of Propagation and Transitions in Complex Systems, particularly in situations implying physical limits as Long Distances Propagation Phenomena (Solitons), Quantum Transitions in Nanostructures, Complex Systems with Great Number of Variables, and infinite Spatio-Temporal Extension of Material Media. This special issue of Mathematical Problems in Engineering seeks original high quality research papers in innovative developments and methods for efficient mathematical approaches for Propagation Phenomena and Transitions in Complex Systems with applications in experimental physics and engineering. The topics include, but are not limited to the following:

• Accurate and efficient mathematical models for long distances propagation phenomena (Solitons)
• Specific methods for solving nonlinear partial differential equations describing wave propagation and transitions in nonlinear optics and optoelectronics
• Mathematical tools for analyzing the dynamics of complex systems with application in nanostructures and microelectronics
• Dynamical models for infinite spatio-temporal extension of material media or for highly repetitive phenomena

Other ideas that achieve the goal of improving the mathematical methods and models describing Propagation Phenomena and Transitions in Complex Systems based on innovative developments and efficient methods are welcome.

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/mpe/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable: