Envelope solitary waves exist and collide head-on without phase shift in a dusty plasma

Abstract

The rarefactive KdV solitary waves in a dusty plasma have been extensively studied analytically and found experimentally in the previous works. Though the envelope solitary wave described by a nonlinear Schrödinger equation (NLSE) has been proposed by using the reductive perturbation method, it is first verified by using the particle-in-cell (PIC) numerical method in this paper. Surprisingly, there is no phase shift after the head on collision between two envelope solitary waves, while it is sure that there are phase shifts of two colliding KdV solitary waves after head on collision.

Formation of solid helical filaments at temperatures of superfluid helium as self-organization phenomena in ultracold dusty plasma

“…Intense scattering of light by microscopic particles allows straightforward observation of particle motions and determination of their coordinates and velocities. This is why a dusty plasma can be used as a convenient tool to study various self-organization phenomena, for example, 3-D 1–5 and 2-D 6 phase transitions, formation of non-linear waves 7,8 , including rogue waves 9 . Dusty plasma provides unique opportunity to carry out studies within much wider range of neutral gas temperature (temperature changes by at least two orders of magnitude in the case of helium gas) as compared to alternative systems, such as clusters composed of water droplets levitating above hot surfaces 10–13 .…”

Head-on collision and overtaking collision between an envelope solitary wave and a KdV solitary wave in a dusty plasma

“…The interaction between a KdV solitary wave and an envelope solitary wave in a dusty plasma will be studied in the present paper by using the one dimensional (1D) PIC method in an infinite background plasma. First we give the 1D dimensionless normalized equations of motion for system 38 40 …”

“…P and Q are functions of system parameters. In the simulation, we choose system parameters as follows: wave number of envelope wave k n = 0.1, then we obtain: P = −0.146, Q = −3.65 40 . One of the envelope solitary wave solution of Eq.…”

“…Interesting results are found when head-on collision between two envelope solitary waves happen. There is a phase shift after a head-on collision between two KdV solitary waves 38 , while there is no phase shift between two envelope solitary waves 40 .…”

“…Recently, the head-on collision between two envelope solitary waves are studied analytically 39 . The head-on collision between two envelope solitary waves has also been studied by using the PIC method 40 . Interesting results are found when head-on collision between two envelope solitary waves happen.…”