scholarly journals Nonlinear Equation in (2+1) Dimensions for a Plasma with Negative Ions

1996 ◽  
Vol 49 (6) ◽  
pp. 1159
Author(s):  
K Roy Chowdhury ◽  
A Roy Chowdhuy
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Nonlinear Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Negative Ions ◽  
System Of Equations ◽  
Nonlinear Wave Propagation ◽  
Reductive Perturbation ◽  
New Form

A new form of coupled nonlinear evolution equation is derived for a plasma with negative ions in (2+1) dimensions. This system of equations can be considered to be an extension of the usual Davey–Stewartson equation. A modified version of reductive perturbation has been used. It is also shown that this set of equations can sustain both cnoidal type and the usual solitary wave-like solution. Such an equation can have important applications in describing nonlinear wave propagation in a dusty plasma.

Rogue Waves and New Multi-wave Solutions of the (2+1)-Dimensional Ito Equation

2015 ◽  
Vol 70 (6) ◽  
pp. 437-443 ◽  
Author(s):  
Ying-hui Tian ◽  
Zheng-de Dai
Keyword(s):  
Solitary Wave ◽  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Extreme Form ◽  
Wave Solutions ◽  
Rogue Wave Solutions ◽  
Ito Equation

AbstractA three-soliton limit method (TSLM) for seeking rogue wave solutions to nonlinear evolution equation (NEE) is proposed. The (2+1)-dimensional Ito equation is used as an example to illustrate the effectiveness of the method. As a result, two rogue waves and a family of new multi-wave solutions are obtained. The result shows that rogue wave can be obtained not only from extreme form of breather solitary wave but also from extreme form of double-breather solitary wave. This is a new and interesting discovery.

scholarly journals Self-focusing of Nonlinear Waves in a Relativistic Plasma with Positive and Negative Ions

1994 ◽  
Vol 47 (6) ◽  
pp. 773 ◽  
Author(s):  
Joydeep Mukherjee ◽  
A Roy Chowdhury
Keyword(s):  
Solitary Wave ◽  
Spatial Variation ◽  
Relativistic Electron ◽  
Nonlinear Wave ◽  
Nonlinear Waves ◽  
Mutual Influence ◽  
Negative Ions ◽  
Relativistic Plasma ◽  
Self Focusing ◽  
Reductive Perturbation

We have analysed the phenomenon of self-focusing of nonlinear waves in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. We also consider the effect of the inertia of the relativistic electron by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schr�dinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider due to the mutual influence of various factors present in the plasma, thus favouring the process of self-focusing.

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