The field of nonlinear optics has developed rapidly since its beginning in 1961. This development is in both the theory of nonlinear effects and the theory of nonlinear interactions in solids, and in the applications of nonlinear devices. This review discusses nonlinear interactions in solids and the resultant nonlinear coupling of electromagnetic waves that leads to second harmonic generation,...

Nonlinear dynamics has changed our view of many biological phenomena; e.g., coexistence of consumer species competing for the same resource [1], biological pattern formation; e.g., clustering and differentiation of mesenchy-mal cells during pre-cartilage messenchymal condensation in chick limb chondrogenesis (bone patterning and formation) [2] and analysis of heart rate variability in healthy a...

In beams which are suf®ciently close to the linear stability limit, a variety of nonlinear wave phenomena are readily observed which can be used to diagnose aspects of the beam dynamics and the machine impedance. We have found that debunched beams in both the Fermilab Main Ring and the Tevatron are marginally stable to longitudinal oscillations and exhibit nonlinear three-wave coupling as well ...

In this paper, chaotic behavior study of a five-cells chopper when it is associated to a nonlinear load is reported. The model of such system is described by a piece-wise smooth six dimensional non-autonomous system. Then, some basic dynamical properties, such as Poincaré mapping, first return map and continuous spectrum are investigated to highlight the main characteristic of this particular c...

In this paper, we treat the turbo decoding algorithm as a dynamical system parameterized by a single parameter that closely approximates the signal-to-noise ratio (SNR). A whole range of phenomena known to occur in nonlinear systems, like the existence of multiple fixed points, oscillatory behavior, bifurcations, chaos and transient chaos are found in the turbo decoding algorithm.

Research in the theory of solitons and its applications has undergone impressive development in recent years and has affected a broad range of fields, including theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups and discrete geometry among others. Robin K. Bullough (21 November 1929–30 August 2008) was a British math...

Nonlinearity is ubiquitous in physical phenomena. Fluid and plasma mechanics, gas dynamics, elasticity, relativity, chemical reactions, combustion, ecology, biomechanics, and many, many other phenomena are all governed by inherently nonlinear equations. (The one notable exception is quantum mechanics, which is a fundamentally linear theory, although recent attempts at grand unification of all f...