An efficient meshless computational technique to simulate nonlinear anomalous reaction–diffusion process in two-dimensional space

Nonlinear Dynamics - In this paper, a numerical simulation of an anomalous reaction–diffusion process in two-dimensional space with a nonlinear source term is presented. An efficient and...     

On the nonlinear dynamics of an ecoepidemic reaction–diffusion model

A reaction–diffusion ecoepidemic model of predator–prey type with a transmissible disease spreading among the predator species only is considered. The longtime behavior of solutions is analyzed and, in particular, absorbing sets in the phase space are determined. Conditions guaranteeing the non existence of non-constant equilibria have been found. Linear and non-linear stability conditions for biologically meaningful equilibria are determined.     

On the Euler flow in ℝ2

We give a global existence and uniqueness theorem for the Euler flow in ² for suitable initial velocity fields, possibly diverging at infinity.     

Dynamical stability in a delayed neural network with reaction–diffusion and coupling

Nonlinear Dynamics - In this paper, a delayed neural network with reaction–diffusion and coupling is considered. The network consists of two sub-networks each with two neurons. In the first...     

Substructures’ coupling with nonlinear connecting elements

Nonlinear Dynamics - The analysis of complex structures is often very challenging since reliable data can only be obtained if the underlying model represents properly the real case. Thus,...     

Nonlinear supratransmission of multibreathers in discrete nonlinear Schrödinger equation with saturable nonlinearities

We show that the transport of vibrational energy in protein chains modeled by the Discrete Nonlinear Schrödinger equation (DNSE) with saturable nonlinearities can be done through the nonlinear supratransmission phenomenon: we find numerically and semi-analytically threshold amplitudes beyond which the wave propagation takes place within the molecular chains. Subsequently, it is shown that the saturable higher order nonlinearity parameter reduces the supratransmission threshold amplitude. We also prove that the discrete gap multibreathers can be transmitted or supratransmitted according to the frequency belonging to the lower forbidden band gap. More precisely, the discrete gap multibreathers are supratransmitted close to the edge of the lower forbidden band.     

Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics

In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.     

Controllable rogue waves in coupled nonlinear Schrödinger equations with varying potentials and nonlinearities

Exact rogue wave solutions, including the first-order rogue wave solutions and the second-order ones, are constructed for the system of two coupled nonlinear Schrödinger (NLS) equations with varying potentials and nonlinearities. The method employed in this paper is the similarity transformation, which allows us to map the inhomogeneous coupled NLS equations with variable coefficients into the integrable Manakov system, whose explicit solutions have been well studied before. The result shows that the rogue wavelike solutions obtained by this transformation are controllable. Concretely, we illustrate how to control the trajectories of wave centers and the evolutions of wave peaks, and analyze the dynamic behaviors of the rogue wavelike solutions.     

Stochastic P-bifurcation in a nonlinear impact oscillator with soft barrier under Ornstein–Uhlenbeck process

Nonlinear Dynamics - This study investigates the effect of randomness in the forcing on a harmonically excited bilinear impact oscillator with a soft barrier. The system parameter range considered...     

Bifurcation in a parametrically excited two-degree-of-freedom nonlinear oscillating system with 1∶2 internal resonance

The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steadystate solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos. Project supported by the National Natural Science Foundation of China (19472046)     

Evolution of optical solitary waves in a generalized nonlinear Schr?dinger equation with variable coefficients

We derive two types of exact analytical solutions in terms of rational-like functions for a generalized nonlinear Schr?dinger equation with variable coefficients via the methods of similarity transformation and direct ansatz. Based on these solutions, several novel optical solitary waves are constructed by selecting appropriate functions, and the main evolution features of these waves are shown by some interesting figures with computer simulation.     

FRP strengthened walls with delaminated regions – Geometrically nonlinear response

The paper studies the geometrically nonlinear behavior of walls that are strengthened with fiber reinforced polymer (FRP) composite materials but include pre-existing delaminated regions. The paper uses an analytical–numerical methodology. Three specially tailored finite elements that correspond to perfectly bonded regions, to delaminated regions where the debonded layers are in contact, and to delaminated regions where the debonded layers are not in contact are presented. All finite elements are based on a high order multi layered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains whereas the contact nonlinearity is handled iteratively. The validity and convergence of the finite element models is demonstrated for each type of element through comparison with closed form analytical solutions available for specific cases. The unified model that combines the three types of finite element is then used for studying the nonlinear behavior of a locally delaminated FRP strengthened wall under in-plane normal and in-plane shear loads. Finally, conclusions regarding the effect of the delamination on the response of the strengthening system, on the conditions that evolve in the bonded region that surrounds the delamination, and on the global response of the multi-layered structure are drawn. Additional conclusions regarding the application of the modeling approach to other delamination sensitive layered structural systems close the paper.     

Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity

Nonlinear Dynamics - In this work, we consider a nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity, which works as a model for the propagation of...     

Soliton-like solutions of a derivative nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers

Under investigation in this paper is a derivative nonlinear Schrödinger equation with variable coefficients, which governs the propagation of the subpicosecond soliton pulses in inhomogeneous optical fibers. Through the nonisospectral Kaup–Newell scheme, the Lax pair is constructed with some constraints on the variable coefficients. Under the integrable conditions, bright one- and multi-soliton-like solutions are derived via the Hirota method. By suitably choosing the dispersion coefficient function, several types of inhomogeneous solitons are obtained in, respectively: (1) exponentially decreasing dispersion profile, (2) linearly decreasing dispersion profile, (3) exponentially increasing dispersion profile, and (4) periodically fluctuating dispersion profile. The intensity of the inhomogeneous soliton can be controlled by means of modifying the loss/gain term. Asymptotic analysis of the two-soliton-like solution is performed, which shows that the changes of the widths, amplitudes, and energies before and after the collision are completely caused by the variable coefficients, but have nothing to do with the collision between two soliton-like envelopes. Through suitable choices of variable coefficients, figures are plotted to illustrate the collision behavior between two inhomogeneous solitons, which has some potential applications in the real optical communication systems.     

The Fast Exact Closure for Jeffery’s equation with diffusion

Jeffery’s equation with diffusion is widely used to predict the motion of concentrated fiber suspensions in flows with low Reynold’s numbers. Unfortunately, the evaluation of the fiber orientation distribution can require excessive computation, which is often avoided by solving the related second order moment tensor equation. This approach requires a ‘closure’ that approximates the distribution function’s fourth order moment tensor from its second order moment tensor. This paper presents the Fast Exact Closure (FEC) which uses conversion tensors to obtain a pair of related ordinary differential equations; avoiding approximations of the higher order moment tensors altogether. The FEC is exact in that when there are no fiber interactions, it exactly solves Jeffery’s equation. Numerical examples for dense fiber suspensions are provided with both a Folgar–Tucker (1984) [3] diffusion term and the recent anisotropic rotary diffusion term proposed by Phelps and Tucker (2009) [9]. Computations demonstrate that the FEC exhibits improved accuracy with computational speeds equivalent to or better than existing closure approximations.     

Advection–diffusion in a porous medium with fractal geometry: fractional transport and crossovers on time scales

Meccanica - In a porous fractal medium, the transport dynamics is sometimes anomalous as well as the crossover between numerous transport regimes occurs. In this paper, we experimentally...