Recently there are so many mathematical models which describe nonlinear phenomena. In some phenomena, the free energy functional is not convex. So, the existence-uniqueness question is sometimes difficult. In order to study such phenomena, let us introduce the new class of abstract nonlinear evolution equations governed by timedependent operators of subdifferential type. In this paper we shall ...

The diverse vocal signals of songbirds are produced by highly coordinated motor patterns of syringeal and respiratory muscles. These muscles control separate sound generators on the right and left side of the duplex vocal organ, the syrinx. Whereas most song is under active neural control, there has been a growing interest in a different class of nonlinear vocalizations consisting of frequency ...

In the theoretical investigation, directly seeking exact solutions for nonlinear partial differential equations has become one of the central themes of perpetual interest in mathematical physics. Nonlinear wave phenomena appear in many fields, such as fluid mechanics, biomathematics, plasma physics, optical fibers, chemical physics, and other areas of engineering. These nonlinear phenomena are ...

2.1 NONLINEAR OPTICAL PHENOMENA Nonlinear optics (NLO) is the study of the interaction of intense electromagnetic field with materials to produce modified fields that are different from the input field in phase, frequency or amplitude. It is a vast area, and undoubtedly one of the most important areas of physics with a diverse range of applications. The field of nonlinear optics is understood t...

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. Recent attempts at grand unification of all fundamenta...