Related papers: Description of Nonlinear Phenomena in the Atmosphe…

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…

Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first…

Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…

A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…

For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…

We carry out the group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The equivalence group of this class is found by the…

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…

This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…

All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

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…

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…

Starting from the Navier--Stokes equations in rotating spherical coordinates with constant density and eddy viscosity varying only with depth, and appropriate, physically motivated boundary conditions, we derive an asymptotic model for the…

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…

I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification…

The paper intends to offer a general overview on what the concept of integrability means for a nonlinear dynamical system and how the symmetry method can be applied for approaching it. After a general part where key problems as direct and…

This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature.…