Collapse in coupled nonlinear Schrödinger equations: Sufficient conditions and applications

Prytula, Vladyslav; Vekslerchik, V. E.; Pérez-Garcı́a, Vı́ctor M.

doi:10.1016/j.physd.2008.07.002

Cited by 14 publications

(7 citation statements)

References 34 publications

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“…Turning now to the blowup phenomenon, in coupled conservative NLS equations it was previously discussed in Refs. without linear coupling and in Ref. with linear coupling (see also Ref.…”

Section: Introduction and Preliminary Observationsmentioning

confidence: 99%

Supercritical Blowup in Coupled Parity‐Time‐Symmetric Nonlinear Schrödinger Equations

2014

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We prove finite time supercritical blowup in a parity‐time‐symmetric system of the two coupled nonlinear Schrödinger (NLS) equations. One of the equations contains gain and the other one contains dissipation such that strengths of the gain and dissipation are equal. We address two cases: in the first model all nonlinear coefficients (i.e., the ones describing self‐action and nonlinear coupling) correspond to attractive (focusing) nonlinearities, and in the second case the NLS equation with gain has attractive nonlinearity while the NLS equation with dissipation has repulsive (defocusing) nonlinearity and the nonlinear coupling is repulsive, as well. The proofs are based on the virial technique arguments. Several particular cases are also illustrated numerically.

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“…Turning now to the blowup phenomenon, in coupled conservative NLS equations it was previously discussed in Refs. without linear coupling and in Ref. with linear coupling (see also Ref.…”

Section: Introduction and Preliminary Observationsmentioning

confidence: 99%

Supercritical Blowup in Coupled Parity‐Time‐Symmetric Nonlinear Schrödinger Equations

2014

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“…This is the limit b → 0, which is addressed in this section. More specifically, we show that the nonlinear dynamics in the presence of the vanishing gauge field for the initial stages of the evolution remains close to the dynamics of the nonlinearly coupled NLS equations (see [12][13][14][15]).…”

Section: Limit Of Vanishing Gauge Potentialmentioning

confidence: 52%

“…also [11], Chapter 9). Two coupled NLS equations without SO coupling (b = 0) were previously addressed in [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup

Dias¹,

Figueira²

2015

Stud Appl Math

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We study solutions of the Cauchy problem for nonlinear Schrödinger system in R 3 with nonlinear coupling and linear coupling modeling synthetic magnetic field in spin-orbit coupled Bose-Einstein condensates. Three main results are presented: a proof of the local existence, a proof of the sufficient condition for the blowup result in finite time for some solutions, and the persistence of the nonlinear dynamics in the limit where the spin-orbit coupling converges to zero.

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“…The polarizations are next coupled via an NLS system of the form (1). More backgrounds about these systems and their applications may be found in [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System

2021

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Systems of coupled nonlinear PDEs are applied in many fields as suitable models for many natural and physical phenomena. This makes them active and attractive subjects for both theoretical and numerical investigations. In the present paper, a symmetric nonlinear Schrödinger (NLS) system is considered for the existence of the steady state solutions by applying a minimizing problem on some modified Nehari manifold. The nonlinear part is a mixture of cubic and superlinear nonlinearities and cubic correlations. Some numerical simulations are also illustrated graphically to confirm the theoretical results.

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Collapse in coupled nonlinear Schrödinger equations: Sufficient conditions and applications

Cited by 14 publications

References 34 publications

Supercritical Blowup in Coupled Parity‐Time‐Symmetric Nonlinear Schrödinger Equations

Supercritical Blowup in Coupled Parity‐Time‐Symmetric Nonlinear Schrödinger Equations

Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup

Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System

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