Localized asymptotic solutions of the self-consistent field equation

Belov, V. V.; Smirnova, E. I.

doi:10.1007/s11006-006-0138-z

Cited by 5 publications

(7 citation statements)

References 3 publications

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“…is a formally asymptotic solution mod O(µ 3/2 ) of original problem (5), which completes the proof of the theorem. L 0 , L 1 , χ 0 , and χ 1 .…”

Section: Lemma 2 Let a Function Of The Form φ(X T µ) = A(µ)e Is(xsupporting

confidence: 60%

“…Asymptotic solutions with this property were constructed in [4], [5] for the Hartree-type equation (with a nonlocal nonlinear interaction) in the three-dimensional Euclidean space:…”

Section: Introductionmentioning

confidence: 99%

“…This effect is possibly destroyed with time already in the framework of our model(5) and even of (7) because the corrections that were neglected in (13) become essential in the case of strong spreading and can prevent the already spread packet from localizing once again.…”

mentioning

confidence: 99%

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Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

et al. 2008

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We consider the nonlinear Schrödinger equation with an integral Hartree-type nonlinearity in a thin quantum waveguide and study the propagation of Gaussian wave packets localized in the spatial variables. In the case of periodically varying waveguide walls, we establish the relation between the behavior of wave packets and the spectral properties of the auxiliary periodic problem for the one-dimensional Schrödinger equation. We show that for a positive value of the nonlinearity parameter, the integral nonlinearity prevents the packet from spreading as it propagates. In addition, we find situations such that the packet is strongly focused periodically in time and space.

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“…is a formally asymptotic solution mod O(µ 3/2 ) of original problem (5), which completes the proof of the theorem. L 0 , L 1 , χ 0 , and χ 1 .…”

Section: Lemma 2 Let a Function Of The Form φ(X T µ) = A(µ)e Is(xsupporting

confidence: 60%

“…Asymptotic solutions with this property were constructed in [4], [5] for the Hartree-type equation (with a nonlocal nonlinear interaction) in the three-dimensional Euclidean space:…”

Section: Introductionmentioning

confidence: 99%

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Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

et al. 2008

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“…In this section we shall analyze the theory of chiral two-form in six dimensions with self-dual three-form field strength 3 . We begin by describing the usual formulation of the theory where we impose the self-duality constraint after deriving the equations of motion from the action.…”

Section: Chiral Two-form In Six Dimensions and Its Dimensional Reduct...mentioning

confidence: 99%

“…Various approaches have been suggested for avoiding this problem. These formulations either break manifest Lorentz invariance [1][2][3], or have infinite number of auxiliary fields [4][5][6][7][8][9][10][11][12], or have a finite number of auxiliary fields with non-polynomial action [13][14][15][16][17][18][19], or require going to one higher dimension [20,21]. Other attempts in this direction can be found in [22,23].…”

Section: Introductionmentioning

confidence: 99%

Self-dual forms: action, Hamiltonian and compactification

Sen

2020

J. Phys. A: Math. Theor.

137

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It has been shown that, by adding an extra free field that decouples from the dynamics, one can construct actions for interacting 2n-form fields with self-dual field strengths in 4n+2 dimensions. In this paper we analyze canonical formulation of these theories, and show that the resulting Hamiltonian reduces to the sum of two Hamiltonians with independent degrees of freedom. One of them is free and has no physical consequence, while the other contains the physical degrees of freedom with the desired interactions. For the special cases of chiral scalars in two dimensions and chiral two form fields in six dimensions, we discuss compactification of these theories respectively on a circle and a two dimensional torus, and show that we recover the expected properties of these systems, including S-duality invariance in four dimensions.1

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Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters

Pereskokov

2014

Theor Math Phys

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Localized asymptotic solutions of the self-consistent field equation

Cited by 5 publications

References 3 publications

Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

Self-dual forms: action, Hamiltonian and compactification

Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters

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