Freak waves in laboratory and space plasmas

Abstract

Abstract. Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ionacoustic waves due to the modulational instability. The second wave mode is the Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves.

Baseband modulation instability as the origin of rogue waves

“…Nevertheless, the conditions under which MI may produce an extreme wave event are not fully understood. A rogue wave may be the result of MI, but conversely not every kind of MI necessarily leads to rogue-wave generation [18,[23][24][25].…”

Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

“…Rogue waves are also called killer waves, freak waves, giant waves, monster waves, or extreme waves, which appeared in nautical mythology, entered the ocean waves [2][3][4], and gradually moved into other fields, such as optics [5][6][7], matter waves [8], superfluids [9], plasmas [10], atmosphere [11], and even finance [12]. The common characteristics and differences in various fields of physics are under discussion [13].…”

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

“…As a fundamental characteristic of many nonlinear dispersive systems, MI is related to the growth of periodic perturbations on an unstable continuous-wave background [24]. A rogue wave may be the result of MI, but not every type of MI results in rogue-wave generation [25][26][27]. One of theoretical researches has revealed the close relationship between rogue waves and baseband MI, i.e., MI whose bandwidth includes components of arbitrarily low frequency [28][29][30].…”