Integrable couplings are coupled systems for the integrable equations, which the given integrable equations as subsystems of coupled systems are contained. The research on integrable couplings has significant theoretical meaning and application value and attracts more and more attention in the mathematics and physics in the last decades. The method and topics on integrable systems and their couplings systems include Hamiltonian structures, conservation laws, exact solution, Darboux transformation, nonlinearization, and so on.

The special issue examines such topics as recent research advances based on the above method and new advance on integrable couplings as well as its application. We invite investigators to contribute original research articles as well as review articles that will stimulate to interpret and understand the generation, properties, and application of the integrable couplings as well as the related problems.

We are particularly interested in articles describing the nonlinear phenomenon with the integrable equations and their couplings systems, such as model of meteorology, water wave model, biology model, finance model, and so on. Potential topics include, but are not limited to:

• Lie algebra and superalgebras and their prolongation
• New generation of continue and discrete integrable couplings
• Hamiltonian structures and conservation laws for integrable systems
• Solution for integrable systems
• Application in fluid mechanics, biology, and finance engineering

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