In this paper, the dynamic simulation for a high pressure regulator is performed to obtain the regulator behavior. To analyze the regulator performance, the equation of motion for inner parts, the continuity equation for diverse chambers and the equation for mass flow rate were derived. Because of nonlinearity and coupling, these equations are solved using numerical methods and the results are ...

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 continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a bosonic field theory which has a cubic anti-hermitian nonlinearity. Thereby it is established that the stationary two-point function spreads superdiffusively.

This note concerns a nonlinear differential equation problem in which both the nonlinearity in the equation and its solution are determined by prescribed data. The question under consideration arises from a study of two-dimensional steady parallel-flows of a perfect fluid governed by Euler’s equations and a free-boundary condition, when the distribution of vorticity is arbitrary but prescribed.

The existence of inertial manifolds for a Smoluchowski equation—a nonlinear and nonlocal Fokker–Planck equation which arises in the modelling of colloidal suspensions—is investigated. The difficulty due to first-order derivatives in the nonlinearity is circumvented by a transformation. Mathematics Subject Classification: 35Kxx, 70Kxx

The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.

We consider pulse and front solutions to a spatially discrete FitzHugh–Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving candidate solutions for the McKean nonlinearity and present and apply solvability conditions necessary for existence. Our equation contains both spatially continuous and discre...

We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation −∆u = f(u) in the whole R , where f ∈ C(R) is a general nonlinearity and N ≥ 1 is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.

This paper studies the Klein-Gordon equation with quadratic nonlinearity. The ansatz approach is used to first obtain the singular soliton solution of the equation along with the corresponding domain restriction. The bifurcation analysis is also carried out. By this analysis, a few more traveling wave solutions are retrieved. The bifurcation phase portraits are also given.

In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein–Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.