Higher order nonlinear evolutions differential equations and their solutions
Nonlinear evolution equations are key instruments for wave modelling in nature and in laboratory. Nonlinearity sometimes triggers so called 'extreme events' in various physical systems. Rogue Waves is one example of extreme events occurring in nonlinear systems. They can appear on the surface of water or in optics. The nonlinear Schroedinger equation is a fundamental equation describing these phenomena. However, higher order terms describing self-steepening and self-frequency shift are also important. In this seminar, I will consider the effects of 'even' and 'odd' perturbing terms in the higher-order equations, and will explain, in particular, how the addition of quintic terms modify the basic NLS solutions.