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Preface; Contents; Contributors; Short Pulse Evolution Equation; 1 Introduction; 2 The Nature of SPEE; 3 Derivation of SPEE; 4 Challenges, Questions, and Conclusions; References; Variants of the Focusing NLS Equation: Derivation, Justification, and Open Problems Related to Filamentation; 1 Introduction; 1.1 Models Without Ionization Processes; 1.2 Models with Ionization Processes; 1.3 Notations; 2 The Maxwell Equations and an Abstract Mathematical Formulation; 2.1 The Maxwell Equations; 2.1.1 The Polarization Response to the Electric Field; 2.1.2 The Case with Charge and Current Density.
2.1.3 Ionization Current Density2.2 Abstract Formulations; 2.2.1 The Case Without Charge nor Current Density; 2.2.2 The Case with Charge and Current Density; 2.3 The Cauchy Problem; 3 Derivation of NLS-Type Equations; 3.1 The Profile Equation; 3.2 The Slowly Varying Envelope Approximation; 3.3 The Full Dispersion Model; 3.4 The NLS Equation; 3.5 The NLS Equation with Improved Dispersion Relation; 3.6 The NLS Equation with Frequency Dependent Polarization; 3.7 Including Ionization Processes; 3.7.1 The Profile Equation; 3.7.2 The Slowly Varying Envelope Approximation.
3.7.3 The NLS Equation with Ionization3.7.4 The Most General Model; 4 Analysis of (3) and (4), and Open Problems; 4.1 The Case of No and Anomalous GVD (Resp. [alpha]_1=0 and [alpha]_1=1); 4.1.1 The Nonlinearity; 4.1.2 Taking the Ionization Process into Account; 4.1.3 The Damping; 4.1.4 Off-Axis Variation of the Group Velocity; 4.1.5 Self-steepening of the Pulse; 4.2 The Case of Normal GVD (i.e., [alpha]_1=-1); 4.3 Mixing Several Phenomena; 4.4 The Vectorial Case; 4.5 The Approximation of the Maxwell Equations over Longer Times; Appendix 1: Nondimensionalization of the Equations.
The Case Without Charge nor Current DensityThe Case with Charge and Current Density; Appendix 2: Explicit Computations for Maxwell's Equations; The Case Without Charge nor Current Density; Without Frequency Dependent Polarization; With Frequency Dependent Polarization; The Case with Charge and Current Density; References; Blowing Up Solutions to the Zakharov System for Langmuir Waves; 1 Introduction; 2 The Scalar Zakharov System; 2.1 Blowup in Finite or Infinite Time; 2.2 Self-similar Blowing Up Solutions; 2.2.1 Dimension d=2; 2.2.2 Dimension d=3; 2.3 Lower Bounds for Rate of Blowup.
2.3.1 Scale Invariance, Criticality, and Local Well-Posedness2.3.2 Finite Energy Solutions: The Two-Dimensional Case; 2.3.3 Infinite Energy Solutions; 3 The Vectorial Zakharov System; References; THz Waveforms and Polarization from Laser Induced Plasmas by Few-Cycle Pulses; 1 Introduction; 2 Generation of CEP Stabilized Few-Cycle Pulses; 2.1 Optical Parametric Amplifier; 2.2 Pulse Compression; 2.3 CEP Stability; 3 Variation of `3́9`42`""̇613A``45`47`""603ATHz Waves in Air Plasma by Few-Cycle Pulses; 3.1 Variation of `3́9`42`""̇613A``45`47`""603ATHz Waveform in Air Plasma.
2.1.3 Ionization Current Density2.2 Abstract Formulations; 2.2.1 The Case Without Charge nor Current Density; 2.2.2 The Case with Charge and Current Density; 2.3 The Cauchy Problem; 3 Derivation of NLS-Type Equations; 3.1 The Profile Equation; 3.2 The Slowly Varying Envelope Approximation; 3.3 The Full Dispersion Model; 3.4 The NLS Equation; 3.5 The NLS Equation with Improved Dispersion Relation; 3.6 The NLS Equation with Frequency Dependent Polarization; 3.7 Including Ionization Processes; 3.7.1 The Profile Equation; 3.7.2 The Slowly Varying Envelope Approximation.
3.7.3 The NLS Equation with Ionization3.7.4 The Most General Model; 4 Analysis of (3) and (4), and Open Problems; 4.1 The Case of No and Anomalous GVD (Resp. [alpha]_1=0 and [alpha]_1=1); 4.1.1 The Nonlinearity; 4.1.2 Taking the Ionization Process into Account; 4.1.3 The Damping; 4.1.4 Off-Axis Variation of the Group Velocity; 4.1.5 Self-steepening of the Pulse; 4.2 The Case of Normal GVD (i.e., [alpha]_1=-1); 4.3 Mixing Several Phenomena; 4.4 The Vectorial Case; 4.5 The Approximation of the Maxwell Equations over Longer Times; Appendix 1: Nondimensionalization of the Equations.
The Case Without Charge nor Current DensityThe Case with Charge and Current Density; Appendix 2: Explicit Computations for Maxwell's Equations; The Case Without Charge nor Current Density; Without Frequency Dependent Polarization; With Frequency Dependent Polarization; The Case with Charge and Current Density; References; Blowing Up Solutions to the Zakharov System for Langmuir Waves; 1 Introduction; 2 The Scalar Zakharov System; 2.1 Blowup in Finite or Infinite Time; 2.2 Self-similar Blowing Up Solutions; 2.2.1 Dimension d=2; 2.2.2 Dimension d=3; 2.3 Lower Bounds for Rate of Blowup.
2.3.1 Scale Invariance, Criticality, and Local Well-Posedness2.3.2 Finite Energy Solutions: The Two-Dimensional Case; 2.3.3 Infinite Energy Solutions; 3 The Vectorial Zakharov System; References; THz Waveforms and Polarization from Laser Induced Plasmas by Few-Cycle Pulses; 1 Introduction; 2 Generation of CEP Stabilized Few-Cycle Pulses; 2.1 Optical Parametric Amplifier; 2.2 Pulse Compression; 2.3 CEP Stability; 3 Variation of `3́9`42`""̇613A``45`47`""603ATHz Waves in Air Plasma by Few-Cycle Pulses; 3.1 Variation of `3́9`42`""̇613A``45`47`""603ATHz Waveform in Air Plasma.