Nonlinear stability of solitons against strong external perturbations

Abstract

We study soliton stability under the action of strong external perturbations. Limits on the weak perturbation approach are established with the help of average Lagrangian methods and full simulations. We found that for the same relative perturbation, larger amplitude solitons develop instability earlier than weaker amplitude solitons.

Nonlinear spatiotemporal stability of solitons against external perturbations

“…Note that unlike the previous exponential ansatz of Ref. [15], the present one preserves accurately the structure of equilibrium solutions. To obtain governing equations for the ansatz variables, called collective variables, we adopt the variational approach.…”

“…In a recent work soliton stability against nonintegrable effects has been investigated [15]. However, proper motion of soliton centroid has not been considered as in all the analyzed cases solitons were taken as vibrating envelopes centered at fixed points.…”

The planetary–exoplanetary environment: A nonlinear perspective

“…Plasma radio emissions generated by Langmuir-ion acoustic turbulence through nonlinear three-wave interactions (Melrose, 1991;Chian and Abalde, 1995;Rizzato et al, 2003) have been observed in planetary foreshocks (Kuncic and Cairns, 2005), type-III solar radio bursts (Lin et al, 1986;Henri et al, 2009) and type-II radio bursts from interplanetary shocks (Ledenev et al, 2008). A schematic diagram depicting the emission of nonthermal radio emissions by nonlinear wave-wave interactions in plasmas, via either a Langmuir-Alfvén turbulence or a Langmuirion acoustic turbulence, is shown in Fig.…”

“…1 shows that nonthermal radio emissions can be produced via a Langmuir-ion acoustic turbulence. This three-wave interaction involves an electron-beam driven Langmuir wave (L), a transverse electromagnetic wave (T) and an ion-acoustic wave (S), which is represented as L T AE S (Melrose, 1991;Chian and Abalde, 1995;Rizzato et al, 2003). It provides an emission mechanism for nonthermal radio emissions in planetary foreshocks and interplanetary medium (Lin et al, 1986;Kuncic and Cairns, 2005;Henri et al, 2009).…”

“…The ordered state is described by a stable periodic orbit (regular attractor) and the chaotic state (chaotic attractor) is described by an infinite set of unstable periodic orbits. The dynamical systems approach to turbulence can elucidate the nonlinear dynamics and structures of the planetary-exoplanetary environment, such as Alfvén turbulence (Chian et al, 1998Rempel and Chian, 2005), Langmuir turbulence (De Oliveira et al, 1995;Chian et al, 1996Chian et al, , 2000Chian et al, , 2002Rizzato et al, 2003) and drift turbulence (He and Chian, 2003;Rempel and Chian, 2007).…”