Dynamic analysis of an aeroelastic airfoil with freeplay nonlinearity by precise integration method based on Padé approximation

Nonlinear Dynamics - An improved precise integration method (PIM) incorporated with Padé approximation (PadéPIM) is proposed, and the aeroelastic behavior of an aeroelastic airfoil with...     

Stability and Extinction for Lotka–Volterra Systems with Infinite Delay

The paper deals with the global stability of a saturated equilibrium \({x^{\ast} = (x_1^{\ast}, \ldots, x_n^{\ast}) \ge 0}\) for a multi-species Lotka–Volterra model with infinite delay. We assume the existence of non-delayed diagonal intraspecific competition terms, but relax the usual conditions of dominance which permit to control the infinite delay effect. Our results also apply to non-autonomous Lotka–Volterra systems without saturated equilibria, by studying the stability of their limiting equations. Some known results in the literature are improved and generalized.     

Computation Formulas of Generalized Inverse Padé Approximants Using for Solution of Integral Equations

For the generalized inverse function-valued Padé approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form. Foundation item: the National Natural Science Foundation of China (19871054) Biography: Gu Chuan-qing (1955-), Professor, Doctor Director     

Vanishing Viscosity with Short Wave–Long Wave Interactions for Systems of Conservation Laws

Motivated by Benney’s general theory, we propose new models for short wave–long wave interactions when the long waves are described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity and short wave–long wave interactions systems by using compactness results from compensated compactness theory and new energy estimates obtained for the coupled systems. We analyze several of the representative examples, such as scalar conservation laws, general symmetric systems, nonlinear elasticity and nonlinear electromagnetism.     

Well-Posedness for Multicomponent Schrödinger–gKdV Systems and Stability of Solitary Waves with Prescribed Mass

In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed \(L^2\)-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger–Korteweg-de Vries systems.     

Stability analysis of cable–bar structures by inverse-power method for eigenvalue analysis with penalization

A numerical method is presented for stability analysis of cable–bar structures. An optimization problem is formulated to find the minimum value of the incremental total potential energy that depends on the direction of the incremental displacements. The penalty method with slack variables is used for representing the discontinuity in member stiffness. The tangent stiffness matrix is shifted to be positive definite so that the minimum of its quadratic form is found by the inverse-power method. It is shown in the numerical examples that the minimum value of the incremental potential energy and the associated displacement increments can be found with good accuracy in about 10 steps of iteration.     

Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays

This paper is concerned with the traveling wave solutions of delayed reaction–diffusion systems. By using Schauder’s fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka–Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka–Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.     

Determination of periodic solutions for nonlinear oscillators with fractional powers by He’s modified Lindstedt-Poincaré method

He’s modified Lindstedt-Poincaré method is applied to nonlinear oscillatiors with fractional powers. Comparison of the obtained results with exact solutions provides confirmation for the validity of He’s modified Lindstedt-Poincaré method.     

Periodic solutions for certain non-smooth oscillators by iterated homotopy perturbation method combined with modified Lindstedt-Poincaré technique

In this paper, a new technique is introduced by combining Homotopy perturbation method and modified Lindstedt-Poincaré technique to obtain the periodic solutions of certain non-smooth oscillators. In this technique, homotopy perturbation method is re-written in iterative form to linearize perturbation process by homotopy, and then, the modified Lindstedt-Poincaré method is utilized to obtain next approximation for each iteration step. We realize that this new technique works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been confirmed and discussed. Only one or two iterations lead to high accuracy of the solutions. The result obtained and comparison with analytical solution and different methods provide confirmation for the validity of the technique.