The nonlinear Schrödinger equation : singular solutions and optical collapse /: singular solutions and optical collapse. (2015)

• Record Type: Book
• Further Information: Note: Gadi Fibich.
• Authors: Fibich, Gadi
• Contents: Derivation of the NLS -- Linear propagation -- Early self-focusing research -- NLS models -- Existence of NLS solutions -- Solitary waves -- Variance identity -- Symmetries and the lens transformation -- Stability of solitary waves -- The explicit critical singular peak-type solution -- The explicit critical singular ring-type solution -- The explicit supercritical singular peak-type solution -- Blowup rate, blowup profile, and power concentration -- The peak-type blowup profile -- Vortex solutions -- NLS on a bounded domain -- Derivation of reduced equations -- Loglog law and adiabatic collapse -- Singular H1 ring-type solutions -- Singular H1 vortex solutions -- Singular H1 peak-type solutions -- Singular standing-ring solutions -- Singular shrinking-ring solutions -- Critical and threshold powers for collapse -- Multiple filamentation -- Nonlinear Geometrical Optics (NGO) method -- Location of singularity -- Computation of solitary waves -- Numerical methods for the NLS -- Effects of spatial discretization -- Modulation theory -- Cubic-quintic and saturated nonlinearities -- Linear and nonlinear damping -- Nonparaxiality and backscattering (nonlinear Helmholtz equation) -- Ultrashort pulses -- Normal and anomalous dispersion -- NGO method for ultrashort pulses with anomalous dispersion -- Continuations beyond the singularity -- Loss of phase and chaotic interactions.
• Publisher Details: Cham : Springer
• Publication Date: 2015
• Extent: 1 online resource (xxxi, 862 pages), illustrations (some color)
• Subjects: 530.12/4; Mathematics; Gross-Pitaevskii equations; Gross-Pitaevskii equations; Science -- Molecular Physics; Science -- Electricity; Science -- Chaotic Behavior in Systems; Atomic & molecular physics; Optical physics; Nonlinear science; Differential equations, partial; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319127484; 3319127489; 3319127470; 9783319127477
• Related ISBNs: 9783319127477
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed March 13, 2015).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.