We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations) under a KP-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrödinger equation.

asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.we have used a general method, based on zakharov integral equation.on the basis of these evolution eq...

In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper...

A T-junction is a fundamental fluid element prevalent in pipe networks of water supplies and power plants. In the present study, a double T-junction was investigated for flow instability and fluid vibration. Both axi-aligned and skewed double T-junctions are examined from viewpoint of flow instability. With single-phase flow in an open-ended double T-junction, fluid vibration is induced in both...

This paper presents a nonlinear model of a clamped-clamped microbeam actuated by an electrostatic load with stretching and thermoelastic effects. The frequency of free vibration is calculated by discretization based on the Differential Quadrature (DQ) Method. The frequency is a complex value due to the thermoelastic effect that dissipates energy. By separating the real and imaginary parts of fr...

We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the formation of regular periodic or quasiperiodic modulations of the polarization. We reveal that such nonlinear nanoparticle arrays can support long-lived standing and ...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...

the static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilever micro-beam are considered. considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent euler-bernoulli beam model is used based on a modified couple stress theory, c...

In this paper, the transverse vibration of a triple-walled carbon nanotube (TWCNT) conveying fluid flow is studied based on the strain/inertia gradient theory with van der Waals interaction taken into consideration. The nanotube is modelled using Euler-Bernoulli beam model and the Galerkin’s method is employed to obtain the CNT complex valued Eigen-frequencies. The effects of the fluid flow tho...