Ebook: Soliton Management in Periodic Systems

During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

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During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

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During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

Content:
Front Matter....Pages i-xii
Introduction....Pages 1-24
Periodically modulated dispersion, and dispersion management: basic results for solitons....Pages 25-50
The split-step model....Pages 51-71
Nonlinearity management for quadratic, cubic, and Bragg-grating solitons....Pages 73-88
Resonant management of one-dimensional solitons in Bose-Einstein condensates....Pages 89-104
Management for channel solitons: a waveguiding-antiwaveguiding system....Pages 105-113
Stabilization of spatial solitons in bulk Kerr media with alternating nonlinearity....Pages 115-119
Stabilization of two-dimensional solitons in Bose-Einstein condensates under Feshbach-resonance management....Pages 121-130
Multidimensional dispersion management....Pages 131-142
Feshbach-resonance management in optical lattices....Pages 143-160
Back Matter....Pages 161-180

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During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

Content:
Front Matter....Pages i-xii
Introduction....Pages 1-24
Periodically modulated dispersion, and dispersion management: basic results for solitons....Pages 25-50
The split-step model....Pages 51-71
Nonlinearity management for quadratic, cubic, and Bragg-grating solitons....Pages 73-88
Resonant management of one-dimensional solitons in Bose-Einstein condensates....Pages 89-104
Management for channel solitons: a waveguiding-antiwaveguiding system....Pages 105-113
Stabilization of spatial solitons in bulk Kerr media with alternating nonlinearity....Pages 115-119
Stabilization of two-dimensional solitons in Bose-Einstein condensates under Feshbach-resonance management....Pages 121-130
Multidimensional dispersion management....Pages 131-142
Feshbach-resonance management in optical lattices....Pages 143-160
Back Matter....Pages 161-180
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