Related papers: Three-wave interactions and strange attractor
Triadic resonance is one mechanism via which internal waves dissipate their energy, often at locations away from their generation sites. In this paper, we perform a combined theoretical and numerical study of triadic resonance in internal…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
Wave turbulence is by nature a multiple time scale problem for which there is a natural asymptotic closure. The main result of this analytical theory is the kinetic equation that describes the long-time statistical behaviour of such…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
Space-time modulation systems have garnered significant attention due to their resemblance to moving-matter systems and promising applications. Unlike conventional moving-matter systems, modulation systems do not involve net motion of…
The chaotic properties of Newton-Leipnik system are discussed from the view point of strange attractors. Previously, two strange attractors of this system were illustrated which occured from two different initial conditions under the same…
The aim of this work is to study trapped waves and their collisions between two topographic obstacles for the forced Korteweg-de Vries equation. Numerical simulations show that solitary waves remain trapped bouncing back and forth between…
Real-world systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin…
The excitation of atomic levels due to interaction with electromagnetic waves became of interest in accelerator physics in relation to high efficiency charge exchange injection into rings for high beam power applications. Usually, the beam…
In wave turbulence, it has been believed that statistical properties are well described by the weak turbulence theory, in which nonlinear interactions among wavenumbers are assumed to be small. In the weak turbulence theory, separation of…
There is a formal correspondence between the isotropic 3-wave kinetic equation and the rate equations for a non-linear fragmentation--aggregation process. We exploit this correspondence to study analytically the time evolution of the wave…
Three-dimensional special relativistic magnetohydrodynamic simulations are performed to investigate properties of the downstream turbulence generated by the interaction between a relativistic shock wave and multiple clumps. We analyze the…
We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schr\"odinger equation for deep-water gravity waves under the effect of wind and viscosity. The evolution of the norm (wave-action) and spectral mean…
We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a…
The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these…
We employ the generic three-wave system, with the $\chi ^{(2)}$ interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs) and three-wave…
In undulatory locomotion, torques along the body are required to overcome external forces from the environment and bend the body. Using a resistive force theory model, we find that the torque from external resistive forces has a traveling…
We have studied the correlated Brownian motion of micron-sized particles suspended in water and confined between two plates. The hydrodynamic interaction between the particles exhibits three anomalies. (i) The transverse coupling is…
Magnetic reconnection is a fundamental mechanism of driving eruptive phenomena of different scales and may be coupled with turbulence as suggested by recent remote-sensing and in-situ observations. However, the specific physics behind the…
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…