Chaotic Spatial Patterns Described by the Extended Fisher–Kolmogorov Equation

Spatial Patterns Described by the Extended Fisher-kolmogorov (efk) Equation: Periodic Solutions

On Gaussian Beams Described by Jacobi's Equation

Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the Červený equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton–Jacobi theory with Jacobi’s equation that connects Riemannian curvature to ge...

Chaoticons described by nonlocal nonlinear Schrödinger equation

It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-lik...

Conservative Control Systems Described by the Schrödinger Equation

An important subclass of well-posed linear systems is formed by the conservative systems. A conservative system is a system for which a certain energy balance equation is satisfied both by its trajectories and those of its dual system. In Malinen et al. [10], a number of algebraic characterizations of conservative linear systems are given in terms of the operators appearing in the state space d...

physical problems described by the equation λu ′′ ′ + u

On the existence of monotonic fronts for a class of physical problems described by the equation λu ′′′ + u ′ = f (u) Abstract We obtain an upper bound on the value of λ for which monotonic front solutions of the equation λu ′′′ + u ′ = f (u) with λ > 0 may exist.