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Dynamical Systems and Nonlinear Waves in Plasmas [Kõva köide]

(Politecnico di Torino, Italy),
  • Formaat: Hardback, 218 pages, kõrgus x laius: 234x156 mm, kaal: 557 g, 8 Illustrations, color; 91 Illustrations, black and white
  • Ilmumisaeg: 10-Sep-2021
  • Kirjastus: CRC Press
  • ISBN-10: 0367487322
  • ISBN-13: 9780367487324
Teised raamatud teemal:
Dynamical Systems and Nonlinear Waves in PlasmasSuurem pilt
  • Formaat: Hardback, 218 pages, kõrgus x laius: 234x156 mm, kaal: 557 g, 8 Illustrations, color; 91 Illustrations, black and white
  • Ilmumisaeg: 10-Sep-2021
  • Kirjastus: CRC Press
  • ISBN-10: 0367487322
  • ISBN-13: 9780367487324
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367487324.html
Märksõnad:
"This book provides clear ideas on dynamical systems and waves in plasmas. It also presents derivation of different nonlinear evolution equations describing nonlinear plasma waves (ion-acoustic, dust-acoustic, dust-ion-acoustic, electron-acoustic) through a perturbative approach. It demonstrates bifurcation behavior of nonlinear and supernonlinear waves characterized by trivial and nontrivial topologies of their phase portraits for the corresponding dynamical systems. Chaotic and hyperchaotic behaviors of various plasma waves are presented in presence or absence of external periodic force. It also provides real applications to NLSE and laser plasma interaction"--

This book provides clear ideas on dynamical systems and waves in plasmas. It also presents derivation of different nonlinear evolution equations describing nonlinear plasma waves (ion-acoustic, dust-acoustic, dust-ion-acoustic, electron-acoustic) through a perturbative approach.



Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media.

It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas.

The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

Preface iv
1 Introduction
1(22)
1.1 Plasma as a state
1(1)
1.2 Plasmas exist in nature
2(2)
1.2.1 Ionosphere
2(1)
1.2.2 Van Allen belts
2(1)
1.2.3 Aurorae
3(1)
1.2.4 Solar corona
3(1)
1.2.5 Core of the sun
3(1)
1.2.6 HII regions
4(1)
1.3 Concept of temperature
4(5)
1.3.1 Existence of several temperatures
7(1)
1.3.2 Electron and ion temperatures
8(1)
1.3.3 Quasineutrality in plasma
8(1)
1.4 Debye length and Debye sphere
9(3)
1.5 Criteria for plasma
12(1)
1.6 Plasma frequency
13(2)
1.7 Applications of plasma
15(1)
1.7.1 Space physics
15(1)
1.7.2 Astrophysics
15(1)
1.7.3 Gas lasers
16(1)
1.7.4 Industrial application
16(1)
1.8 Fluid description of plasma
16(6)
1.8.1 Maxwell's equation
17(1)
1.8.2 Equation of motion
17(4)
1.8.5 Poisson equation
21(1)
References
22(1)
2 Dynamical Systems
23(16)
2.1 Introduction to dynamical systems
23(15)
2.1.1 One-dimensional system
23(1)
2.1.1.1 Equilibrium point and its stability
24(1)
2.1.1.2 Trajectory and phase portrait
24(1)
2.1.1.3 Example
24(1)
2.1.2 Linear stability analysis
24(2)
2.1.2.1 Example
26(1)
2.1.3 Potentials
26(1)
2.1.3.1 Example
27(1)
2.1.3.2 Example
27(1)
2.1.4 Bifurcations
28(1)
2.1.5 Linear system in two-dimension
29(2)
2.1.5.1 Example
31(1)
2.1.6 Phase plane analysis
32(1)
2.1.6.1 Nonlinear system in two-dimension
33(1)
2.1.6.2 Conservative system
34(1)
2.1.6.3 Example
34(2)
2.1.6.4 Example
36(1)
2.1.6.5 Hamiltonian system
37(1)
2.1.6.6 Example
37(1)
References
38(1)
3 Waves in Plasmas
39(49)
3.1 Introduction to wave modes
39(32)
3.1.1 Ion-acoustic (IA) waves
39(1)
3.1.2 Dust-acoustic (DA) waves
40(1)
3.1.3 Dust-ion-acoustic (DIA) waves
41(1)
3.1.4 Upper hybrid wave
42(4)
3.1.5 Electrostatic cyclotron waves
46(4)
3.1.6 Lower hybrid wave
50(6)
3.2.1 The KdV equation
56(4)
3.2.2 The Burgers equation
60(3)
3.2.3 The KP equation
63(4)
3.2.4 The ZK and mZK equations
67(4)
3.3 Analytical wave solutions of evolution equations
71(16)
3.3.1 Analytical wave solution of the KdV equation
71(2)
3.3.2 Analytical wave solution of the mKdV equation
73(2)
3.3.3 Analytical wave solution of the KP equation
75(2)
3.3.4 Analytical wave solution of the mKP equation
77(3)
3.3.5 Analytical wave solution of the ZK equation
80(2)
3.3.6 Analytical wave solution of the mZK equation
82(2)
3.3.7 Analytical wave solution of the Burgers equation
84(3)
References
87(1)
4 Bifurcation of Small Amplitude Waves in Plasmas
88(38)
4.1 Introduction
88(1)
4.2 Bifurcation of ion-acoustic waves with small amplitude
89(7)
4.2.1 Basic equations
89(1)
4.2.2 Derivation of the KdV equation
90(1)
4.2.3 Formation of dynamical system
91(1)
4.2.4 Phase plane analysis
91(2)
4.2.5 Wave solutions
93(3)
4.3 Bifurcation of dust-ion-acoustic waves with small amplitude
96(9)
4.3.1 Governing equations
96(2)
4.3.2 Derivation of the KP equation
98(1)
4.3.3 Formation of dynamical system and phase portraits
99(3)
4.3.4 Wave solutions
102(3)
4.4 Bifurcation of dust-acoustic waves with small amplitude
105(8)
4.4.1 Basic equations
106(1)
4.4.2 Derivation of the Burgers equation
107(1)
4.4.3 Formation of dynamical system and phase portraits
108(1)
4.4.4 Wave solutions
109(4)
4.5 Bifurcation of electron-acoustic waves with small amplitude
113(8)
4.5.1 Basic equations
114(1)
4.5.2 Derivation of the KdV equation
114(2)
4.5.3 Formation of dynamical system and phase portraits
116(1)
4.5.4 Wave solutions
117(4)
References
121(5)
5 Bifurcation of Arbitrary Amplitude Waves in Plasmas
126(28)
5.1 Introduction
126(1)
5.2 Bifurcation of ion-acoustic waves with arbitrary amplitude
127(5)
5.2.1 Basic equations
127(1)
5.2.2 Formation of dynamical system and phase portraits
127(4)
5.2.3 Wave solutions
131(1)
5.3 Bifurcation of dust-ion-acoustic waves with arbitrary amplitude
132(8)
5.3.1 Basic equations
132(2)
5.3.2 Formation of dynamical system and phase portraits
134(5)
5.3.3 Wave solutions
139(1)
5.4 Bifurcation of dust-acoustic waves with arbitrary amplitude
140(3)
5.4.1 Basic equations
140(1)
5.4.2 Formation of dynamical system and phase portraits
140(3)
5.4.3 Wave solutions
143(1)
5.5 Bifurcation of electron-acoustic waves with arbitrary amplitude
143(9)
5.5.1 Basic equations
146(1)
5.5.2 Formation of dynamical system and phase portraits
146(3)
5.5.3 Wave solutions
149(3)
References
152(2)
6 Bifurcation Analysis of Supernonlinear Waves
154(26)
6.1 Introduction: supernonlinear waves
154(1)
6.1.1 Different kind of trajectories
154(1)
6.2 Bifurcation of supernonlinear ion-acoustic waves
155(7)
6.2.1 Basic equations
155(3)
6.2.2 Modified KdV equation
158(1)
6.2.3 Formation of dynamical system and phase portraits
159(2)
6.2.4 Wave solutions
161(1)
6.3 Bifurcation of supernonlinear dust-acoustic waves
162(7)
6.3.1 Basic equations
162(1)
6.3.2 Formation of dynamical system and phase portraits
163(1)
6.3.3 Wave solutions
164(5)
6.4 Bifurcation of supernonlinear electron-acoustic waves (EAWs)
169(9)
6.4.1 Basic equations
170(1)
6.4.2 The evolution equation and dynamical system
171(2)
6.4.3 Wave solutions
173(5)
References
178(2)
7 Chaos, Multistability and Stable Oscillation in Plasmas
180(25)
7.1 Chaos in a conservative dusty plasma
180(7)
7.1.1 Basic equations
182(1)
7.1.2 Multiperiodic, quasiperiodic and chaotic oscillations
182(5)
7.2 Multistability of electron-acoustic waves
187(4)
7.2.1 Basic equations
187(1)
7.2.2 Multistability
188(3)
7.3 Stable oscillation in a dissipative plasma
191(9)
7.3.1 Model equations
192(1)
7.3.2 The KdV-Burgers equation
193(2)
7.3.3 Stability analysis of DAWs
195(5)
References
200(5)
Index 205
Asit Saha is Assistant Professor (Research) in the Department of Mathematics, Sikkim Manipal Institute of Technology under Sikkim Manipal University, India. He received University Medal and Kiran Chandra Bhattacharya Medal for his MSc programme from University of North Bengal in 2005. He received his Ph.D. degree in 2016 from Visva-Bharati, India. He received Emerging Researcher Award in 2019 for his research contribution from Sikkim Manipal University. He is serving as an Editor for "The European Physical Journal Plus" since June, 2019. His research areas cover bifurcation, chaotic, hyperchaotic and multistability behaviours of waves in plasmas and various nonlinear fields. His group is known as the first to apply the theory of planar dynamical systems in plasma waves.

Santo Banerjee was working as Associate Professor, in the Institute for Mathematical Research (INSPEM), University Putra Malaysia, Malaysia till 2020, and also a founder member of the Malaysia-Italy Centre of Excellence in Mathematical Science, UPM, Malaysia. He is now associated with the Department of Mathematics, Politecnico di Torino, Italy. His research is mainly concerned with Nonlinear Dynamics, Chaos, Complexity and Secure Communication. He is a Managing Editor of EPJ Plus (Springer).