Related papers: Variational nonlinear WKB in the Eulerian frame
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of…
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
Solutions of nonlinear multi-component Euler-Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem. Nonlocal structures are an essential feature…
We consider a generic Hamiltonian system of nonlinear interacting waves with 3-wave interactions. In the kinetic regime of wave turbulence, which assumes weak nonlinearity and large system size, the relevant observable associated with the…
The standard classical description of non-laminar charge particle beams in paraxial approximation is extended to the context of two wave theories. The first theory is the so-called Thermal Wave Model (TWM) that interprets the paraxial…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
In this paper, we characterized resonant interaction of weakly nonlinear hyperbolic waves in gas dynamics with a real gas background. An asymptotic approach is used to study the interaction between waves, governed by the Euler equations of…
The buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
The one-dimension Russo--Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Reductions of the model to finite component systems are derived. Stability of the bubbly…
The Berry phase is a geometric phase that is important in explaining topological quantum phenomena. The Berry phase is also important in non-perturbative phenomena, as the imaginary part of the phase explains the non-perturbative…
We apply the method of slowly-varying amplitudes of the electrical and magnet fields to integro-differential system of nonlinear Maxwell equations. The equations are reduced to system of differential Nonlinear Maxwell amplitude Equations…
We analytically investigate the nonlinear response of a damped doubly clamped nanomechanical beam under static longitudinal compression which is excited to transverse vibrations. Starting from a continuous elasticity model for the beam, we…
We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the…
In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the…
A formal methodology for developing variational principles corresponding to a given nonlinear PDE system is discussed. The scheme is demonstrated in the context of the incompressible Navier-Stokes equations, systems of first-order…
Nonlinear hydrodynamic equations for visco-elastic media are discussed. We start from the recently derived fully hydrodynamic nonlinear description of permanent elasticity that utilizes the (Eulerian) strain tensor. The reversible quadratic…