Related papers: Phase space analysis of higher-order dispersive eq…
We present a wave packet analysis of a class of possibly degenerate parabolic equations with variable coefficients. As a consequence, we prove local wellposedness of the corresponding Cauchy problem in spaces of low regularity, namely the…
This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
Using a Fourier spectral method, we provide a detailed numerically investigation of dispersive Schr\"odinger type equations involving a fractional Laplacian. By an appropriate choice of the dispersive exponent, both mass and energy sub- and…
The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the…
We propose the use of an orthogonal wave packet basis to analyze the low-energy physics of interacting electron systems with short range order. We give an introduction to wave packets and the related phase space representation of fermion…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
The interaction of charged particles, moving in a uniform magnetic field, with a plane-polarized gravitational wave is considered using the Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact…
The study of wave propagation in chains of anharmonic periodic systems is of fundamental importance to understand the response of dynamical absorbers of vibrations and acoustic metamaterials working in nonlinear regime. Here, we derive an…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
This study employs spectral methods to capture the behaviour of wave equation with dispersive-nonlinearity. We describe the evolution of hump initial data and track the conservation of the mass and energy functionals. The…
We establish sharp pointwise kernel estimates and dispersive properties for the wave equation on noncompact symmetric spaces of general rank. This is achieved by combining the stationary phase method and the Hadamard parametrix, and in…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
We complement previous studies of an ion coupled with an optical cavity in the dispersive regime, for a model which exhibits bistability of different configurations in the semiclassical description. Our approach is based on a truncated…
We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
In one-dimensional case the search for presence of the anomalous phenomena in multiplicity distributions is usually performed in frame of the horizontal, vertical and mixed types of the analysis. We show that if the data involve a…