Related papers: Equations of 3-th waves hierarchy
By writing the complete set of $3 + 1$ (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and…
In this paper we study different Hamiltonian systems with polynomial and rational Hamiltonians associated with the generic third Painlev\'e equation and present explicit birational transformations relating them.
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a…
Recently, two different proofs for large and intermediate-size solitary waves of the nonlocally dispersive Whitham equation have been presented, using either global bifurcation theory or the limit of waves of large period. We give here a…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space-time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
In this paper, we introduce a novel category of central compact schemes inspired by existing cell-node and cell-centered compact finite difference schemes, that offer a superior spectral resolution for solving the dispersive wave equation.…
The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, with…
This article is dedicated to unifying the framework used to derive the Wiener--Hopf equations arising from some discrete and continuous wave diffraction problems.The main tools are the discrete Green's identity and the appropriate notion of…
In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer system of fluids with rigid-lid condition for the…