Related papers: Nonlinear waves, differential resultant, computer …
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
In this paper, we investigate the lifespan estimates of classical solutions of the initial value problems for semilinear wave equations of derivative type with characteristic weights in one space dimension. Such equations provide us basic…
Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these…
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 nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of…
The lagrangian of the Kaluza-Klein theory, in its simplest five-dimensional version, should include not only the scalar curvature R, but also the quadratic Gauss-Bonnet invariant. The general lagrangian is computed and the resulting…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing,…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
We study the evolution equations for gravitational waves, which are derived using the full metric to raise and lower indices. This method ensures full consistency between the Ricci tensor and all gauge restrictions and requirements, and…
We introduce a probabilistic representation for solutions of quasilinear wave equation with analytic nonlinearities. We use stochastic cascades to prove existence and uniqueness of the solution.
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…
We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical $C$- and $S$-integrable Partial Differential Equations (PDEs). Generalizations of…
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…