Related papers: On an adjustment to the Fowler equation

We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schroedinger equation with harmonic forces. We also argue…

In this paper, we present an extensive study of linearly forced isotropic turbulence. By using an analytical method, we identified two parametric choices that are new to our knowledge. We proved that the underlying nonlinear dynamical…

Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by…

Based on the wormlike chain model, a coarse-grained description of the nonlinear dynamics of a weakly bending semiflexible polymer is developed. By means of a multiple scale perturbation analysis, a length-scale separation inherent to the…

We develop a tool in order to analyse the dynamics of differentiable flows with singularities. It provides an abstract model for the local dynamics that can be used in order to control the size of invariant manifolds. This work is the first…

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…

In this paper we propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $\mathbb{R}^n$ with $n\geq 2$. We give a reformulation of the Euler equations as a differential…

We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process…

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We study properties of these filtering flows and provide…

The non-linear way the anomalous dimension parameter has been introduced in the historic first version of the exact renormalization group equation is compared to current practice. A simple expression for the exactly marginal redundant…

In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics…

Compared to barchan dunes, the morphodynamics of linear dunes that elongate on a non-erodible bed is barely investigated by means of laboratory experiments or numerical simulations. Using a cellular automaton model, we study the elongation…

The hydrodynamical model of quantum mechanics based on the Schroedinger equation is combined with the magnetohydrodynamical term to form so called quantum magnetohydrodynamic equation. It is shown that the quantum correction to the Alfven…

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…

An explicit expression in terms of canonical variables is obtained for the Hamiltonian functional determining the fully nonlinear dynamics of two-dimensional potential flows of an ideal fluid with a free surface over an arbitrary nonuniform…

We consider the class of physical theories whose dynamics are given by natural equations, which are partial differential equations determined by a functor from the category of n-manifolds, for some n, to the category of fiber bundles,…

The dune skeleton model is a reduced model to describe the formation process and dynamics of characteristic types of dunes emerging under unidirectional steady wind. Using this model, we study the dependency of the morphodynamics of…

We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…

We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…