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The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field…
This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…
A cylindrical container partially filled with a liquid in orbital shaking motion, i.e. in circular translation with fixed orientation with respect to an inertial frame of reference, generates, along with a rotating sloshing wave, a mean…
Laboratory experimental results are presented for nonlinear Internal Solitary Waves (ISW) propagation in deep water configuration with miscible fluids. The results are validated against direct numerical simulations and traveling wave exact…
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
We note that the non-orthogonality of states and their coincidence at the degeneracy point are both admitted by nonlinear Hermitian systems and linear non-Hermitian systems. These striking characteristics motivate us to re-investigate the…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria for systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The…
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…
We construct a special asymptotic solution for the forced Boussinesq equation. The perturbation is small and oscillates with a slowly varied frequency. The slow passage through the resonance generates waves with the finite amplitude. This…
We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the WKB representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of…
Asymptotic reductions of a defocusing nonlocal nonlinear Schr\"{o}dinger model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its…
In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the…
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…
A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson…