Wen-Rong Sun
The control of wave propagation, particularly the quest for unidirectional transport, plays an important role in photonics and metamaterial science. While nonreciprocity is known to enable unidirectional amplification and stabilize complex…
The interplay of periodic driving and dissipation is a fundamental feature of nonequilibrium physics. We elaborate a scenario for the formation of dissipative multi-spot excitations (MSEs) in Kerr cavities, modeled by the one- and…
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…
In this work we report on the emergence of a novel type of solitary waves, viz., time-localized solitons in integrable and non-integrable variants of the massive Thirring models and in the three-wave resonant-interaction system, which are…
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…
The instabilities of the nontrivial phase elliptic solutions in a repulsive Bose-Einstein condensate (BEC) with a periodic potential are investigated. Based on the defocusing nonlinear Schr\"{o}dinger (NLS) equation with an elliptic…
We consider the instability and stability of periodic stationary solutions to the classical \phi^4 equation numerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and…
Using the integrability of the sinh-Gordon equation, we demonstrate the spectral stability of its elliptic solutions. By constructing a Lyapunov functional using higher-order conserved quantities of the sinh-Gordon equation, we show that…
The stability of the elliptic solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation is studied. The orbital stability of the cmKdV equation was established in [19] when the periodic orbits do not oscillate around…
We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrodinger equations…