1 Introduction 1
References 3
2 Nonlinear Schr？dinger's Equation 5
2.1 Derivation of NLSE 5
2.1.1 Limitations of conventional solitons 9
2.1.2 Dispersion-management 10
2.1.3 Mathematical formulation 11
2.2 Integrals of motion 15
2.3 Soliton perturbation theory 18
2.3.1 Perturbation terms 19
2.4 Variational principle 20
2.4.1 Perturbation terms 21
References 22
3 Polarization Preserving Fibers 27
3.1 Introduction 27
3.2 Integrals of motion 28
3.2.1 Gaussian pulses 29
3.2.2 Super-Gaussian pulses 30
3.2.3 Super-Sech pulses 32
3.3 Variational principle 35
3.3.1 Gaussian pulses 35
3.3.2 Super-Gaussian pulses 36
3.4 Perturbation terms 36
3.4.1 Gaussian pulses 37
3.4.2 Super-Gaussian pulses 37
3.5 Stochastic perturbation 38
References 42
4 Birefringent Fibers 45
4.1 Introduction 45
4.2 Integrals of motion 47
4.2.1 Gaussian pulses 49
4.2.2 Super-Gaussian pulses 49
4.3 Variational principle 50
4.3.1 Gaussian pulses 52
4.3.2 Super-Gaussian pulses 53
4.4 Perturbation terms 55
4.4.1 Gaussian pulses 57
4.4.2 Super-Gaussian pulses 58
References 60
5 Multiple Channels 63
5.1 Introduction 63
5.2 Integrals of motion 64
5.2.1 Gaussian pulses 66
5.2.2 Super-Gaussian pulses 67
5.3 Variational principle 68
5.3.1 Gaussian pulses 69
5.3.2 Super-Gaussian pulses 70
5.4 Perturbation terms 70
5.4.1 Gaussian pulses 73
5.4.2 Super-Gaussian pulses 74
References 75
6 Optical Crosstalk 77
6.1 In-band crosstalk 78
6.2 Gaussian optical pulse 80
6.2.1 Bit error rate 84
6.3 Sech optical pulse 85
6.4 Super-Sech optical pulse 88
References 93
7 Gabitov-Turitsyn Equation 95
7.1 Introduction 95
7.2 Polarization-preserving fibers 96
7.2.1 Special solutions 99
7.3 Birefringent fibers 100
7.4 DWDM system 104
7.5 Properties of the kernel 107
7.5.1 Lossless Case 108
7.5.2 Lossy Case 108
References 109
8 Quasi-linear Pulses 111
8 1 Introduction 111
8.2 Polarization-preserving fibers 112
8.2.1 Lossless system 112
8.2.2 Lossy system 115
8.3 Birefringent fibers 121
8.3.1 Lossless system 122
8.3.2 lossy system 124
8.4 Multiple channels 129
8.4.1 Lossless system 129
8.4.2 Lossy system 131
References 134
9 Higher Order Gabitov-Turitsyn Equations 137
9.1 Introduction 137
9.2 Polarization preserving fibers 137
9.3 Birefringent fibers 142
9.4 DWDM systems 149
References 154
Index 157