The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

In this study, we investigate the oscillation phenomena in a random-coupled network of hard-type oscillators whose nonlinear characteristics are represented by fifth-power polynomials. Recently, we have shown that the chaotic phenomena are seen in the network with softtype oscillators whose nonlinear characteristics are represented by third-power polynomials. In this paper, for the networks wit...

The response of strongly nonlinear dynamic systems to stochastic excitation exhibits many interesting characteristics. In this paper, excitation forms like white noise and Gaussian band limited noise are applied to a bilinear system. The nonlinear characteristics cannot be represented sufficiently accurate using statistical linearization techniques. Integration techniques have to be used. The e...

Resonant phenomena for a class of nonlinear systems, which can be described by a single-degree-of-freedom (sdof) model with a polynomial-type nonlinear stiffness, are investigated using nonlinear output frequency response functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for this class of nonlinear systems using the NOFRF concept, and the effects of damping on ...

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to secondorder phase transitions, from superconductivity, superfluidity and Bose-Einstein condensation to liquid crystals and strings in field theory. Our goal is to give an overview of various phenomena described the c...

Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, th...