Related papers: Description of Nonlinear Phenomena in the Atmosphe…
In this paper, we formulate an N=2 supersymmetric extension of a hydrodynamic-type system involving Riemann invariants. The supersymmetric version is constructed by means of a superspace and superfield formalism, using bosonic superfields,…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
A powerful method for solving non-linear first-order ordinary differential equations, which is based on geometrical understanding of the corresponding dynamics of the so called Lie systems, is developed. This method allows us not only to…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new…
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…
We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…
Several classes of self-similar, spherically symmetric solutions of relativistic wave equation with nonlinear term of the form sign(\phi) are presented. They are constructed from cubic polynomials in the scale invariant variable t/r. One…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this article, we construct new solitary wave solutions for the…
Exact solutions describing Rossby waves and vortices in ocean propagating along the zonal direction at a constant velocity are considered for the (3+1)-dimensional nonlinear Charney-Obukhov equation. In the first part of our work, we give…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…
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 apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed…
We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density…
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…