We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond harmonic forcing. This reconciles nonmodal nature these mechanisms and need for center manifold project leading-order dynamics. Under hypothesis strong nonnormality, we take advantage fact that small operator per...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

The nonlinear stages of the recently uncovered instability due to insoluble surfactant at the interface between two fluids in a creeping plane Couette flow are investigated for the case when one of the fluids is a thin film and the other one is a much thicker layer. Numerical simulation of strongly nonlinear longwave evolution equations which couple the film thickness and the surfactant concent...

Nonlinear optical responses provide a powerful way to understand the microscopic interactions between laser fields and matter. They are critical for plenty of applications, such as in lasers, integrated photonic circuits, biosensing medical tools. However, most materials exhibit weak nonlinearities or long response times when they interact with intense fields. Here, we strongly couple exciton o...

We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose-Einstein condensates. In this c...

Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the si...