Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 2004"

TL;DR: In this article, a general method, dynamical systems method for solving linear and non-linear ill-posed problems in a Hilbert space is presented, which consists of the construction of a nonlinear dynamical system, that is, a Cauchy problem, which has the following properties: (1) it has a global solution, (2) this solution tends to a limit as time tends to infinity, (3)

TL;DR: In this paper, a single-degree-of-freedom mechanical oscillator is shown to exhibit chaotic motions. This is not expected in a single degree of freedom system and the occurrence of chaos becomes possible because the friction model contains one internal variable.

TL;DR: In this paper, the equilibrium and stability of thin plate axially traveling with high-speed is investigated. But the results are reducible to the linear, von Karman and nonlinear membrane theories.

TL;DR: The study shows how to stabilize the system, while having a satisfactory performance, even in the case when some of the motor parameters were uncertain, even after the system experienced a dynamic bifurcation at high frequencies.

TL;DR: In this paper, the authors investigated the motion and stability of a four-wheel-steering (4WS) vehicle with the nonlinearity of the lateral tyre forces, and the effects of the steering mechanism.

TL;DR: In this paper, it was shown that the infinite-dimensional equivalence Lie algebra L E has three functionally independent differential invariants of the second order for the family of nonlinear wave equations formulated in the title.

TL;DR: In this paper, the authors find the bright and dark solutions of nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields by applying the inverse scattering method and selecting appropriate transformation.

TL;DR: In this article, by using an infinitesimal technique, they find invariants of a family of nonlinear wave equations and apply these invariants to the linearization problem.

TL;DR: In this paper, a deterministic mathematical model for the transmission dynamics of HIV infection in the presence of a preventive vaccine is considered, and the existence and threshold conditions for their stability are theoretically investigated.

TL;DR: The weighted ENO (WENO) technique is analyzed, introduced by Liu et al. in the context of conservation laws, and applied to the compression of images, using multiresolution techniques.

TL;DR: It is shown that the way in which the derivatives are approximated is crucial for the success of the method, and a new way to compute them is presented that makes the scheme adequate for non-smooth data.

TL;DR: In this article, the authors give a definition of an admitted Lie group for functional differential equations and some examples of applications of this definition are studied, including finding an equivalence group, contact and Lie-Backlund transformations.

TL;DR: In this paper, the bases of differential invariants for infinite-dimensional Lie groups, admitted by the Navier-Stokes and gas dynamics equations, are calculated and the possibilities of bases application to construct differentially invariant solutions are shown.

TL;DR: In this paper, the authors presented a numerical model for solving the two-layer exchange problem through channels with irregular geometry both in breadth and depth and the obtaining of maximal exchange solutions as defined by Armi and Farmer.

TL;DR: In this paper, the existence of homoclinic orbits for the truncation equations is established by Mel'nikov analysis and geometric singular perturbation theory, and a perturbed higher-order nonlinear Schrodinger equation with periodic boundary condition is considered.

TL;DR: In this article, a generalized cell mapping method is developed to refine persistent and transient self-cycling sets, respectively, on the basis of their definitions in the cell state space.

TL;DR: The aim is to calculate the generators of the equivalence group for one of the known models and, using the equivalences generators, specify arbitrary elements, find additional symmetries and calculate group invariant solutions.

TL;DR: In this article, the Darboux transformation method is applied to construct exactly solvable periodic pseudoscalar potentials for the one-dimensional Dirac equation, and the underlying quadratic supersymmetry is revealed.

TL;DR: In this article, the static pressure and surface shear forces on a rotating, umbrella-deformed disk in an open shroud are investigated numerically to develop a proper dynamical model for investigation of the self-excited vibration of the disk.

TL;DR: In this article, a closed-form solution for rigid-body motions of two-dimensional traveling, sagged cables with a nonlinear geometrical constraint is developed, which shows that the rigid body motions are always stable even if the translation speed is over the critical speed.

TL;DR: In this paper, the authors explore an approach to the constitutive equations for the Reynolds stress, assuming that it is determined by the history of the mean deformation of turbulence but has a fading memory.

TL;DR: A complete description of the whole set of such operators, as well as subsets of operators of a given order, and translation-invariant operators is obtained in this article.

TL;DR: In this article, the characteristics of the dynamic systems exerted by discontinuous piecewise constant forces are investigated and compared to the systems under continuous exertions, diverse behaviors of the systems with discontinuous exertions are found.

TL;DR: In this paper, some aspects of application of symmetry groups for analysis of nonlinear dynamics of gas bubbles in liquid: scaling bubble pulsation, dynamics of tethered bubble, distribution of coagulating bubbles.

TL;DR: The analytical results indicate that the elastodynamic response in the mechanism with clearance connections cannot be well controlled by using a single control method, and so the feasibility of combined control method is proved.

TL;DR: In this paper, a two-dimensional particle-laden turbulent flow of an air stream carrying small spheres is simulated over a backward-facing step, where the continuous phase is performed by the method of large eddy simulation while the particle phase is solved by a Lagrangian method.

TL;DR: In this paper, an alternative approach to using phase plots, bifurcation diagrams, or Fourier analysis for characterizing the various responses displayed by time-delayed feedback oscillators of both autonomous and non-autonomous types is presented.

TL;DR: The optimal efficacy level of anti-retroviral therapy needed to eradicate HIV from the body of an HIV-infected individual is obtained.

TL;DR: In this paper, the Coulomb friction model was used to model the frictional forces at a beam with a frictional joint and the steady-state solutions of the system to sinusoidal excitations were analyzed.

TL;DR: In this article, the authors derived the one-dimensional optimal system of the nonlinear partial differential equation due to Scott and Stevenson which describes the two-phase fluid flow of a medium compacting under gravity.