New linearization technique that reduces the thirdand fifth-order intermodulation products is proposed in this paper. It suggests the injection of second harmonics (IM2) at the amplifier input whereas the IM2 signals and fourth-order nonlinear signals (IM2+IM4) are fed into the amplifier output. The reduction of the thirdand fifth-order intermodulation products has been achieved by applying a n...

In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

A new iterative method of the fourth order for solving nonlinear equations of the form f(x) = 0 is derived. The comparison with other existing methods is performed regarding the computational efficiency and numerical examples. The fourth-order derivative free method for the simultaneous calculation of all polynomial zeros, arising from the proposed method, is also studied. AMS Mathematics Subje...

For n > 2, we establish the smooth effects for the solutions of the linear fourth order Shrödinger equation in anisotropic Lebesgue spaces with k-decomposition. Using these estimates, we study the Cauchy problem for the fourth order nonlinear Schrödinger equations with three order derivatives and obtain the global well posedness for this problem with small data in modulation space M 9/2 2,1 (R ).

Purely dispersive equations as the Korteweg-de Vries and the nonlinear Schrödinger equation in the limit of small dispersion have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral methods is benefic...

Abstract. Purely dispersive equations, such as the Korteweg-de Vries and the nonlinear Schrödinger equations in the limit of small dispersion, have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral ...

The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves in Kerr media, and describes a range of important phenomena in nonlinear optics and in other areas. In our previous work, we developed a fourth order method for its numerical solution that involved an iterative solver based on freezing the nonlinearity. The method enabled a direct simulation of nonlinear self...

The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves in Kerr media, and describes a range of important phenomena in nonlinear optics and in other areas. In our previous work, we developed a fourth order method for its numerical solution that involved an iterative solver based on freezing the nonlinearity. The method enabled a direct simulation of nonlinear self...

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...