In this talk I will discuss (1+1) D completely integrable partial differential equations that; in particular, I will consider the Korteweg--de Vries equation and the Kaup--Broer system with both weak and strong capillarity. I will discuss solitary waves or 1-soliton solutions to these equations, discuss a nonlinear superposition principal that allows the calculation of what are called N-soliton solutions, and then consider various classes of solutions that can be produced as a limit of these solutions and N goes to infinity. I will also discuss the periodic and quasiperiodic solutions. I will discuss recent approaches based on the theory of Riemann--Hilbert problems and singular integral equations. I will give some motivation for this work based on the goal of modeling a soliton gas, and provide a brief literature review of some recent experimental results on soliton gasses in hydrodynamics. Speaker(s): Patrik Nabelek (Oregon State University)