Nonlinearity Saturation as a Singular Perturbation of the Nonlinear Schrödinger Equation
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Publication:2794980
DOI10.1137/15M1024974zbMath1344.35135MaRDI QIDQ2794980
Jordan Allen-Flowers, K. B. Glasner
Publication date: 18 March 2016
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Singular perturbations in context of PDEs (35B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Multiple scale methods for ordinary differential equations (34E13) Soliton solutions (35C08)
Related Items (3)
On asymptotic dynamics for \(L^2\) critical generalized KdV equations with a saturated perturbation ⋮ On continuation properties after blow-up time for \(L^2\)-critical gKdV equations ⋮ Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity
Cites Work
- Unnamed Item
- Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
- Interactions of solitons in nonintegrable systems: direct perturbation method and applications
- A perturbational approach to the two-soliton systems
- Limit behavior of saturated approximations of nonlinear Schrödinger equation
- On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- The effects of normal dispersion on collapse events
- Perturbation of solitons with non-Kerr law nonlinearity.
- Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states
- Internal modes of envelope solitons
- On the analytical theory for stationary self-focusing of radiation
- New singular solutions of the nonlinear Schrödinger equation
- Continuations of the nonlinear Schrödinger equation beyond the singularity
- Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems
- Patterns of Propagating Pulses
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
- Linearized instability for nonlinear schrödinger and klein-gordon equations
- On uniqueness and continuation properties after blow‐up time of self‐similar solutions of nonlinear schrödinger equation with critical exponent and critical mass
- Eigenvalues, and instabilities of solitary waves
- Why are solitons stable?
- On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation
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