I= SOCIO – ECONOMIC CONSEQUENCES OF RETURN MIGRATION AND THE ADJUSTMENT PROBLEMS IN PUNJAB Title of Thesis


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Title of Thesis

COUPLED NON-LINEAR WAVES IN PIEZOELECTRIC SEMICONDUCTOR PLASMA

Author(s)

Ghazala Anwar

Institute/University/Department Details

University of the Punjab, Lahore / Centre Of Excellence In Solid State Physics

Session

1998

Subject

Education

Number of Pages

95

 

Keywords (Extracted from title, table of contents and abstract of thesis)

Non-Linear Waves, Piezoelectric Semiconductor Plasma, Helicon-Acoustic Waves, Parametric Instability,

 

Abstract

We have considered coupled non-linear waves in a piezoelectric semiconductor plasma. We consider a number of non-linear wave interactions in the present thesis. Firstly we consider the modulational instability/stability of coupled helicon-acoustic waves. We use the Klylov-Bogoluibov-Mitropolski technique of multiple scale analysis to arrive at the non-linear Schrodinger equation which gives the behavior of above mentioned waves. Physical parameters of InSb are used to investigate numerically whether the wave is modulationally stable or unstable. Secondly we investigate a parametric wave interaction in a piezoelectric semiconductor plasma. The three waves involved in the parametric excitation are the pump wave a coupled upper hybrid-ocoustic wave and extraordinary wave. An expression for the growth of the unstable mode is derived and an expression for the threshold electric field for the onset of the instability is also derived. We have numerically investigate the dependence of threshold electric field for different values of the background parameters for InSb and have given a numerical estimation of the growth rate. Finally we have considered the chaotic evolution of three parametrically interacting waves in a piezoelectric semiconductor plasma. The evolution equation has been derived using the coupled mode theory. The waves are an ordinary wave, extraordinary wave and coupled upper hybrid-acoustic wave. The ordinary wave is a growing wave and the other two are damped modes. The equations are transformed and put in a standard form and made dimensionless by suitable substitution of new variables. Finally a set of three equations is obtained. The real and imaginary parts of the equations are then separated. The three imaginary equations can be reduced to one resulting in a system of four equations. Analytical investigation is made of the stationary points. The evolution of equations for various parameters values is done numerically. Time series analysis and phase space plots of the chaotic evolution of the amplitude are also investigated numerically. Lyapunov exponents are computed and the results are presented graphically.

 

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    Table of Contents  

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1 1 INTRODUCTION 1

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2 2 MODULATIONAL STABILITY/INSTABILITY OF COUPLED NON-LINEAR HELICON-ACOUSTIC WAVES 26

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3 3 Parametric Excitation of Coupled Upper Hybrid-Acoustic Wave and An Extraordinary Wave 45

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4 4 CHAOTIC EVOLUTION OF A PARAMETRIC INSTABILITY 62

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5 5 CONCLUSION

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6 6 FIGURES

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7 7 REFERENCES

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