A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

In the present work, the Rayleigh-Taylor instability of two rotating superposed magnetized fluids within the presence of a vertical or a horizontal magnetic flux has been investigated. The nonlinear theory is applied, by solving the equation of motion and uses the acceptable nonlinear boundary conditions. However, the nonlinear characteristic equation within the elevation parameter is obtained....

In the paper, a auxiliary equation expansion method and its a lgorithm is proposed by studying a second order nonlinear ordinary differential equation with a six-degree term.The method is applied to the generalized derivative Schrödinger equation .As a result,some new exact traveling wave solution are obtained which singular solutions,triangular periodic wave solution and Jacobian elliptic func...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

Recently there has been a lot of interest in studying the global attractivity, the boundedness character, and the periodicity nature of nonlinear difference equations. In [5, 6, 8] some global convergence results were established which can be applied to nonlinear difference equations in proving that every solution of these equations converges to a periodic solution (which need not necessarily b...

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained. Keywords—Neutral functional differential equation, higher order, periodic solution, coincidence degree theory

The exact solution of the anti-symmetric quadratic truly nonlinear oscillator is derived from the first integral of the nonlinear differential equation which governs the behaviour of this oscillator. This exact solution is expressed as a piecewise function including Jacobi elliptic cosine functions. The Fourier series expansion of the exact solution is also analyzed and its coefficients are com...

A variational method given by Ritz has been applied to the Zakharov equation to construct an analytical solution. The solution of Zakharov equation gives a good description of both linear and nonlinear evolutions of instabilities generated in waves due to modulation. The spatially periodic trial function is chosen in the form of combination of Jacobian elliptic functions with the dependence of ...

In this paper we study the asymptotic behavior of the solution of the new class of the nonlinear rational Difference Equations. Namely, we consider the stability, boundedness, and periodicity of the solution. Moreover we give the periodic character of solutions of these equations, which is not familiar. We do not know a similar feature for other class of the nonlinear rational Difference Equati...

We present a chaotic frequency-modulated microwave source that is governed by a simple, first-order nonlinear delay differential equation. When a sinusoidal nonlinearity is incorporated, the dynamical behaviors range from fixed-point to periodic to chaotic, depending on the feedback strength. When the sinusoidal nonlinearity is replaced by a binary nonlinearity, the system exhibits a complex pe...