Related papers: Nonlinear wave interaction problems in three dimen…
In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…
Complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluid. Resonance three-wave interaction processes -- decay instability and confluence of two waves -- are shown to play a key role in the weakly…
We propose a new regularization method for constructing a shock wave type solution with nonsmooth front (interaction of shock waves) for quasilinear equations in the one-dimensional case.
A parallelized three-dimensional (3D) boundary element method is used to simulate the interaction between an incoming solitary wave and a 3D submerged horizontal plate under the assumption of potential flow. The numerical setup follows…
Although extreme or freak waves are repeatedly measured in the oceans, their origin is largely unknown. The interaction of different water waves is seen as one reason for their emergence. One way to consider nonlinear waves in deep water is…
In this work we presented a derivation of the quantum hydrodynamic equations for neutral bosons. We considered short range interaction between particles. This interaction consist binary interaction $U(\textbf{r}_{i},\textbf{r}_{j})$ and…
Nonlinear interaction of three acoustic waves in a sandy sediment is studied in the frequency range where there is a considerable wave velocity dispersion. The possibility of an experimental observation of the generation of a sound wave by…
We consider the Hartree equation with a smooth kernel and an external potential, in the semiclassical regime. We analyze the propagation of two initial wave packets, and show different possible effects of the interaction, according to the…
It is shown that nonlinear three-wave interaction, described by vector-product type nonlinearities, in pair plasmas implies much more restrictive conditions for a double energy transfer, as compared to electron-ion plasmas.
A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the resulting d'Alembert-Hamilton system are obtained.
We present classification of Q-conditional symmetries for the two-dimensional nonlinear wave equations and the reductions corresponding to these nonlinear symmetries. Classification of inequivalent reductions is discussed.
We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition…
We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, L\"u, and Qi systems. We show…
The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging…
Resonant mode interactions in weakly nonlinear multi-dimensional lattices and related effects are described. We concentrate on formal description of the phenomenon and consider as examples mode interactions and evolution equations for…
Semiclassical methods are used to study the nonlinear interaction of light in vacuum in the context of four wave mixing. This study is motivated by a desire to investigate the possibility of using recently developed powerful ultrashort…
We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the…
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…