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We consider instability and localized patterns arising from long wave-short wave (LWSW) resonance in the non-integrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to…
Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are…
We investigate the statistics of rogue waves occurring in the inverse cascade of surface gravity wave turbulence. In such statistically homogeneous, stationary and isotropic wave fields, low-frequency waves are generated by nonlinear…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The modulational instability of nonlinearly interacting spatially incoherent Stokes waves is analyzed. Starting from a pair of nonlinear Schroedinger equations, we derive a coupled set of wave-kinetic equations by using the Wigner transform…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is…
In recent studies on wake stability, it has been observed that a simple linear stability analysis applied to the mean flow instead of the basic flow, could give an accurate prediction of the global mode selected frequency, although these…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based…
Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at…
Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order…
Stop-and-go waves are commonly observed in traffic and pedestrian flows. In most traffic models they occur through a phase transition after fine tuning of parameters when the model has unstable homogeneous solutions. Inertia effects are…
We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…
Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic…
Comparisons of experimental data with numerical predictions of a classical model indicate that an excited hydrogen atom in a pulsed microwave electric field exhibits a nonclassical increase of stability over a relatively wide range of…
To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…
We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric…
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A…
We describe the emergence and interactions of breather modes and resonant wave modes within a two-dimensional ring-like oscillator chain in a microcanonical situation. Our analytical results identify different dynamical regimes…