Nonlinear waves inPT-symmetric systems

Reaction-diffusion Systems and Nonlinear Waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

Complex Billiard Hamiltonian Systems and Nonlinear Waves

There is a deep connection between solutions of nonlinear equations and both geodesic flows and billiards on Riemannian manifolds. For example, in Alber, Camassa, Holm and Marsden [1995], a link between umbilic geodesics and billiards on n-dimensional quadrics and new soliton-like solutions of nonlinear equations in the Dym hierarchy was investigated. The geodesic flows provide the spatial x-fl...

Nonlinear Waves and Solitons in Physical Systems

Advances in nonlinear science have been plentiful in recent years. In particular, interest in nonlinear wave propagation continues to grow, stimulated by new applications, such as ber optic communication systems, as well as the many classical unresolved issues of uid dynamics. What is arguably the turning point for the modern perspective of nonlinear systems took place at Los Alamos over forty ...

On Nonlinear Water Waves in a Channel

Mixing in Symmetric Holmboe Waves

Direct simulations are used to study turbulence and mixing in Holmboe waves. Previous results showing that mixing in Holmboe waves is comparable to that found in the better-known Kelvin–Helmholtz (KH) billows are extended to cover a range of stratification levels. Mixing efficiency is discussed in detail, as are effective diffusivities of buoyancy and momentum. Entrainment rates are compared wi...