Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra

1988 ◽  
Vol 29 (8) ◽  
pp. 1807-1813 ◽  
Author(s):  
P. G. L. Leach ◽  
F. M. Mahomed
Keyword(s):  
First Integral ◽  
Maximal Subalgebra

Soliton turbulence in electronegative plasma due to head-on collision of multi solitons

2020 ◽  
Vol 75 (12) ◽  
pp. 999-1007
Author(s):  
Rustam Ali ◽  
Anjali Sharma ◽  
Prasanta Chatterjee
Keyword(s):  
Wave Field ◽  
Soliton Solutions ◽  
Negative Ions ◽  
First Integral ◽  
Statistical Properties ◽  
Charged Dust ◽  
Bilinear Method ◽  
Electronegative Plasma ◽  
Kdv Equations ◽  
First Four Moments

AbstractHead-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

scholarly journals Electrostatic wave breaking limit in a cold electronegative plasma with non-Maxwellian electrons

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
I. S. Elkamash ◽  
I. Kourakis
Keyword(s):  
Wave Breaking ◽  
Density Ratio ◽  
Negative Ions ◽  
First Integral ◽  
Energy Balance Equation ◽  
Plasma Parameters ◽  
Ion Density ◽  
Electrostatic Wave ◽  
Nonthermal Electrons ◽  
Electronegative Plasma

AbstractA one-dimensional multifluid hydrodynamic model has been adopted as basis for an investigation of the role of suprathermal electrons on the wave breaking amplitude limit for electrostatic excitations propagating in an electronegative plasma. A three-component plasma is considered, consisting of two inertial cold ion populations of opposite signs, evolving against a uniform background of (non-Maxwellian) electrons. A kappa-type (non-Maxwellian) distribution function is adopted for the electrons. By employing a traveling wave approximation, the first integral for the fluid-dynamical system has been derived, in the form of a pseudo-energy balance equation, and analyzed. The effect of intrinsic plasma parameters (namely the ion density ratio, the ion mass ratio, and the superthermal index of the nonthermal electrons) on the wave breaking amplitude limit is explored, by analyzing the phase space topology of the associated pseudopotential function. Our results are relevant to particle acceleration in Space environments and to recent experiments based on plasma-based accelerator schemes, where the simultaneous presence of negative ions and nonthermal electrons may be observed.

scholarly journals An Analytical Solution for Non-Linear Viscoelastic Impact

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1849
Author(s):  
Stelian Alaci ◽  
Constantin Filote ◽  
Florina-Carmen Ciornei ◽  
Oana Vasilica Grosu ◽  
Maria Simona Raboaca
Keyword(s):  
Analytical Solution ◽  
Hysteresis Loop ◽  
Viscoelastic Model ◽  
First Integral ◽  
Coefficient Of Restitution ◽  
Contact Period ◽  
Maximum Deformation ◽  
Impact Parameters ◽  
Simplified Algorithm ◽  
The Moment

The paper presents an analytical solution for the centric viscoelastic impact of two smooth balls. The contact period has two phases, compression and restitution, delimited by the moment corresponding to maximum deformation. The motion of the system is described by a nonlinear Hunt–Crossley equation that, when compared to the linear model, presents the advantage of a hysteresis loop closing in origin. There is only a single available equation obtained from the theorem of momentum. In order to solve the problem, in the literature, there are accepted different supplementary hypotheses based on energy considerations. In the present paper, the differential equation is written under a convenient form; it is shown that it can be integrated and a first integral is found—this being the main asset of the work. Then, all impact parameters can be calculated. The effect of coefficient of restitution upon all collision characteristics is emphasized, presenting importance for the compliant materials, in the domain of small coefficients of restitution. The results (variations of approach, velocity, force vs. time and hysteresis loop) are compared to two models due to Lankarani and Flores. For quasi-elastic collisions, the results are practically the same for the three models. For smaller values of the coefficient of restitution, the results of the present paper are in good agreement only to the Flores model. The simplified algorithm for the calculus of viscoelastic impact parameters is also presented. This algorithm avoids the large calculus volume required by solving the transcendental equations and definite integrals present in the mathematical model. The method proposed, based on the viscoelastic model given by Hunt and Crossley, can be extended to the elasto–visco–plastic nonlinear impact model.

scholarly journals The First Integral Method for Solving Maccari’s System

2011 ◽  
Vol 02 (02) ◽  
pp. 258-263 ◽  
Author(s):  
Davood Rostamy ◽  
Fatemeh Zabihi ◽  
Kobra Karimi ◽  
Siamak Khalehoghli
Keyword(s):  
Integral Method ◽  
First Integral ◽  
First Integral Method

scholarly journals Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
Yong Huang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Constant Coefficient ◽  
Wave Solution ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

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