In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...

We consider the periodic nonlinear Schrödinger equation with nonlinearity given by |u|p−1u for odd p>1 in dimension 1. first establish that difference between evolution and a phase rotation of linear is smoother space. then study forced damped defocusing equations above type an analogous smoothing statement extends globally time. As corollary we both existence smoothness global attractors energy

In this article, nonlinear propagation of envelope gravity waves is studied in baroclinic atmosphere. The classical (2 + 1) dimensional nonlinear Schrödinger (NLS) equation can be derived by using the multiple-scale, perturbation method. Further, via the semi-inverse method, the Euler–Lagrange equation and Agrawal’s method, the time–space fractional (2 + 1) dimensional nonlinear Schrödinger (FN...

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of bi-Hamiltonian methods in [A. S. Fokas, Phys. D 87 (1995), 145–150]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as...

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coe cient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for...

4. Nonlinear phenomena 4.1. Second-order nonlinear phenomena 4.2. Third-order nonlinear phenomena 4.3. Stimulated Raman scattering 4.4. Stimulated Brillouin scattering 4.5. Four-wave mixing (FWM) 4.6. Self-phase modulation (SPM) 4.7. Cross phase modulation (XPM) 4.8. Theoretical description of GVD phenomenon and self-phase modulation 4.8.1. Nonlinear Schrödinger equation 4.8.2. Inclusion of the...

In the current study, the effects of Casimir force and squeeze film damping on pull-in instability and dynamic behavior of electrostatically actuated nano and micro electromechanical systems are investigated separately. Linear elastic membrane theory is used to model the static and dynamic behavior of the system for strip, annular and disk geometries. Squeeze film damping is modeled using nonli...