In this paper, a variable coefficient generalized dispersive water-wave system which can model the propagation of the long weakly nonlinear and weakly dispersive surface waves of variable depth in shallow water is presented. With the aid of symbolic computation and using the generalized (G ′ G )-expansion method, the exact traveling wave solutions of this system are obtained. It is shown that t...

As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a "die") is in practice limited by the appearance of "melt fracture" instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical...

We consider a novel asymptotic limit of model equations proposed to describe the formation of localised states in a vertically vibrated layer of granular material or viscoelastic fluid. In physical terms, the asymptotic limit is motivated by experimental observations that localised states (‘oscillons’) arise when regions of weak excitation are nevertheless able to expel material rapidly enough ...

The gravitational evolution of the genus of the density field in large-scale structure is analytically studied in a weakly nonlinear regime using second-order perturbation theory. Weakly nonlinear evolution produces asymmetry in the symmetric genus curve for Gaussian initial density field. The effect of smoothing the density field in perturbation theory on the genus curve is also evaluated and ...

In this paper we study the use of pseudorandom test techniques for linear and nonlinear devices, in particular Micro Electro Mechanical Systems (MEMS). These test techniques lead to practical BuiltIn-Self-Test techniques (BIST). We will first present the pseudorandom test technique for Linear Time Invariant (LTI) systems. Next, we will illustrate and evaluate the application of these techniques...

Spectra of nonlinear waves in infinite-dimensional Hamiltonian systems are investigated. We establish a connection via the Krein signature between the number of negative directions of the second variation of the energy and the number of potentially unstable eigenvalues of the linearization about a nonlinear wave. We apply our results to determine the effect of symmetry-breaking on the spectral ...

The concept of occasionally weakly compatible (shortly, owc) mappings introduced by Al-Thagafi and Shahzad [2], which is more general than the concept of weakly compatible maps. In this paper, we prove a common fixed point theorem for owc mappings in Menger space using arbitrary continuous t-norm for a nonlinear case. Full text

We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...

In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in cone metric space. Our results extends the result of A.Bhatt, et al.[A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal., 73(2010) 176-182]. Mathematics Subject Classification: Primary: 47H10, 54H25

As a statistical measure of large-scale structure of the universe, the genus number is presented in analytic form for realistic non-Gaussian distributions, i.e., weakly non-Gaussian, lognormal and chi-square distributions. These formulae are compared with the results of N-body simulation. It is shown that the weakly non-Gaussian formula describes the behavior of genus in weakly nonlinear regime...