Ion acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equation in quantum plasma

2016 ◽  
Vol 40 (5) ◽  
pp. 1598-1607 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Solitary Wave ◽  
Burgers Equation ◽  
Quantum Plasma ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Ion Acoustic

Stability of ion acoustic solitary waves in a magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution

2013 ◽  
Vol 80 (1) ◽  
pp. 89-112
Author(s):  
Jayasree Das ◽  
Anup Bandyopadhyay ◽  
K. P. Das
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Solitary Wave ◽  
Velocity Distribution ◽  
Plasma Phys ◽  
Solitary Wave Solutions ◽  
Long Wavelength ◽  
Zk Equation ◽  
Wave Solutions ◽  
Ion Acoustic

AbstractSchamel's modified Korteweg-de Vries–Zakharov–Kuznetsov (S-ZK) equation, governing the behavior of long wavelength, weak nonlinear ion acoustic waves propagating obliquely to an external uniform static magnetic field in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, admits solitary wave solutions having a sech4 profile. The higher order stability of this solitary wave solution of the S-ZK equation has been analyzed with the help of multiple-scale perturbation expansion method of Allen and Rowlands (Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413; 1995 J. Plasma Phys. 53, 63). The growth rate of instability is obtained correct to the order k2, where k is the wave number of a long wavelength plane wave perturbation. It is found that the lowest order (at the order k) instability condition is strongly sensitive to the angle of propagation (δ) of the solitary wave with the external uniform static magnetic field, whereas at the next order (at the order k2) the solitary wave solutions of the S-ZK equation are unstable irrespective of δ. It is also found that the growth rate of instability up to the order k2 for the electrons having Boltzmann distribution is higher than that of the non-thermal electrons having vortex-like distribution for any fixed δ.

scholarly journals Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhigang Yao ◽  
Huayong Xie ◽  
Hui Jie
Keyword(s):  
Solitary Wave ◽  
Rogue Wave ◽  
Kdv Equation ◽  
Auxiliary Function ◽  
Mixed Solution ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Trilinear Form ◽  
Wave Solutions

Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

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