Related papers: Analytic solutions for nonlinear waves in coupled …
Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a…
In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations. Small amplitude waves are studied within the linearization approximation…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We develop a full theoretical analysis of the nonlinear interactions of the two polarizations of a waveguide by means of a vectorial model of pulse propagation which applies to high index subwavelength waveguides. In such waveguides there…
This paper is concerned with the study of the main wave interactions in a system of conservation laws in geochemical modeling. We study the modeling of the chemical complexes on the rock surface. The presence of stable surface complexes…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
Using Lie group theory we construct explicit solitary wave solutions of coupled nonlinear Schrodinger systems with spatially inhomogeneous nonlinearities. We present the general theory, use it to construct different families of explicit…
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the…
Partial-wave analysis is one step in a process connecting experimental measurements to the N* states we are studying. Progress has been made in the area of `model-independent' analysis. However, more model-dependent approaches are needed to…
We apply the version of the method of simplest equation called modified method of simplest equation for obtaining exact traveling wave solutions of a class of equations that contain as particular case a nonlinear PDE that models shallow…
In this paper we present a generalized analytical solution to the generalized state equations of coupled second-order non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These are used to model nodal-line dynamics of coherent fields output by…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…
We consider a system of NLS with cubic interactions arising in nonlinear optics without Galilean symmetry. The absence of Galilean symmetry can lead to many difficulties, such as global existence and blowup problems; see [Comm. Partial…
For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model…