Showing papers in "Physica D: Nonlinear Phenomena in 1988"

TL;DR: In this article, the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval was measured using a self-similarity property.

TL;DR: In this article, the authors compare and contrast the approaches taken by Greenberg, Zykov, Fife, Krinskii and others, with particular emphasis on the case of rotating spiral waves, and discuss some possible extensions of the singular perturbation approach to propagating wave surfaces in three-dimensional space.

TL;DR: In this article, it was shown that wave functions of quantum systems as ħ → 0 have an extra density near unstable periodic trajectories of the classical problem, where the average wave function square is represented as the sum over a finite number of periodic trajectory.

TL;DR: In this article, the existence of travelling wave solutions to a fifth order partial differential equation, which is a formal asymptotic approximation for water waves with surface tension, was proved.

TL;DR: In this paper, an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations was derived using a new version of the Sobolev-Lieb-Thirring inequality.

TL;DR: In this article, the authors studied the nonlinear Schrodinger equation with an attractive linear potential: i ϕ t = -Δϕ + (V(x) − |ϕ| 2σ )ϕ, 0 (n−2) (NLS), which arises in the mathematical description of phenomena in nonlinear optics and plasma physics Nonlinear bound states are finite energy localized solutions which, if dynamically stable, play an important role in the structure of general solutions of NLS.

TL;DR: In this paper, the stability of a solitary wave solution of the Korteweg-de Vries equation was investigated when a fifth order spatial derivative term is added, and it was shown that the solution ceases to be strictly localized but develops an infinite oscillating tail.

TL;DR: In this paper, the transition to turbulence in a one-dimensional array of maps coupled by diffusion is shown to display critical properties similar to those of directed percolation, supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties.

TL;DR: In this paper, the authors studied phase-locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies and derived an exact expression for the probability of phase locking in a linear chain of such oscillators.

TL;DR: In this article, it was shown that symmetry-increasing bifurcation in the discrete dynamics of symmetric mappings is possible (and is perhaps generic) and that a new attractor should have greater symmetry.

TL;DR: In this article, the motion of the central filament of a scroll wave in excitable medium is investigated. But the authors assume that two-dimensional spiral solutions are known and use these solutions to produce slowly varying scroll waves in three-dimensional space.

TL;DR: In this article, the main attention is focused on the localization and ergodicity in classically fully chaotic quantum models, and on related statistical properties of energy spectra as well as of eigenfunctions.

TL;DR: An infinite family of rational solutions of the integrable version of the Boussinesq system ∗ u t + w x + uu x = 0, w t + u xxx + (uw) x = 1 and the associated higher-order flows is constructed in this article.

TL;DR: For the cubic Schrodinger equation in two dimensions, this paper constructed a family of singular solutions by perturbing slightly the dimension d = 2 tod > 2, where d is the dimension of the dimension in which the singular solution is chosen.

TL;DR: In this paper, a method of dynamic rescaling of variables is used to investigate numerically the nature of the focusing singularities of the cubic and quintic Schrodinger equations in two and three dimensions and describe their universal properties.

TL;DR: In this article, the dispersion relation for periodic wave train solutions of diffusion-reaction equations modeling the Belousov-Zhabotinskii reaction was calculated using perturbation and numerical methods.

TL;DR: In this article, the role of symmetry in the Taylor vortex flow and Hopf bifurcation theory was investigated for a range of raduis ratios 0.43 ≤ η≤0.98.

TL;DR: In this paper, the structure and velocity of dislocations are calculated near threshold using amplitude equations appropriate for systems with an axial anisotropy, and the nucleation process of dislocation pairs is discussed by analyzing the threshold solution that describes the nucleus barrier.

TL;DR: In this article, the steady states and their stabilities give a foundation for understanding the dynamics of the Kuramoto-Sivashinsky equation, and a singular perturbation calculation of traveling waves near bifurcation is carried out.

TL;DR: In this article, it was shown that the existence of an analytic invariant in addition to the natural ones (momentum, energy and number of particles) leads to the presence of infinitely many such invariants.

TL;DR: In this article, a method to linearize the initial value problem of the Painleve equations IV, V is given, which involves formulating a Riemann-Hilbert boundary value problem on intersecting lines for the inverse monodromy problem.

TL;DR: In this article, the authors suggest that the transport properties and dissipation rates of a wide class of turbulent flows are determined by the random occurrence of coherent events which correspond to certain orbits which are called homoclinic excursions in the high dimensional strange attractor.

TL;DR: In this paper, the straddle orbit method is used to obtain all the basic sets on a basin boundary, which are then used to untangle the topology of the basin boundaries in the five-dimensional phase space.

TL;DR: In this paper, the complex time analytic structure of the Lorenz system in non-integrable parameter regimes is studied and the special sets of parameter values for which one (time-dependent) integral of motion exists.

TL;DR: In this paper, a constructive method for approximating attractors is presented, where the approximate sets are parts of algebraic sets and they can approximate the attractor at an arbitrary high level of accuracy.

TL;DR: In this article, the authors obtained periodic solutions of the differential equation for periodic forcing of a lightly damped pendulum on the alternative hypotheses that (i) the contributions of second and higher harmonics to the average Lagrangian are negligible or (ii) the solution is close to that for free oscillations.

TL;DR: In this article, the authors presented numerical and theoretical results of resonance kink-antikink (K K ) interactions in the classical one-dimensional space Higgs theory and found two-bounce K K interactions with the number of small oscillations between K K bounces up to 35 in the initial kink velocity interval.

TL;DR: In this paper, the amplitude equation is derived within the framework of a multiple-scale perturbation theory and a particular example of this class of nonlocal dynamics is also treated numerically.

TL;DR: In this paper, the effect of a bias A 0 on the Bonhoeffer-van der Pol oscillator was investigated numerically and the frequency-locked intervals exhibited complete devil's staircase similar to the one observed in Belousov-Zhabotinsky reaction.

TL;DR: In this article, a perturbation theory is developed for slowly varying fully nonlinear wavetrains (i.e., solutions which appear locally as travelling waves, but with frequencies and wavelengths which may vary widely on long length and time scales).