Stability of charged solitons

Kumar, Ajit; Nisichenko, V. P.; Rybakov, Yu. P.

doi:10.1007/bf00670060

Cited by 19 publications

(16 citation statements)

References 4 publications

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“…so that (3.32) As a preparatory step, following the papers (Movchan 1960, Kumar, Nisichenko andMakhankov 1990) According to the general theorem in the theory of stability (Zubov 1957;Malkin 1962) The proof was based on the apparent negativeness of the second variation (derivative) in some neighbourhood of static soliton solutions under scale perturbations 6<p = xio;u.…”

Section: Example 31 Complex Scalar Fields With Harmonic Time-dependmentioning

confidence: 99%

The Skyrme Model

Makhankov

Rybakov

Sanyuk

1993

Springer Series in Nuclear and Particle Physics

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Section: Example 31 Complex Scalar Fields With Harmonic Time-dependmentioning

confidence: 99%

The Skyrme Model

Makhankov

Rybakov

Sanyuk

1993

Springer Series in Nuclear and Particle Physics

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“…where ξ( x) = a( x) + b * ( x) and η( x) = a( x) − b * ( x). The structure of solutions (39) and (44), together with the form of nonlinear equation of motion (8), suggests that the nonlinear overlap term between these modes κ × (t, x) has the form…”

Section: Overlap Terms Between Oscillation and Nonoscillation Modesmentioning

confidence: 99%

“…where the real parameter α ≪ 1 is introduced for convenience and can be considered as the expansion parameter (in such a case, the functions ψ 1,n (t, x) and ψ 2,n (t, x) can be considered to be of the order of f (r)). Here ψ 1,n (t, x) satisfies the linearized equation of motion, following from (8). The standard ansatz for ψ 1,n (t, x) has the form [16,17]…”

Section: Introductionmentioning

confidence: 99%

“…In what follows, I consider only the classically stable Q-balls such that dQ 0 dω < 0 [7][8][9][10][11] (for the proof of the classical stability criterion based on the use of only the linearized equations of motion for perturbations, like in [12][13][14] for the nonlinear Schrödinger equation, see [15]). The energy of the system is…”

Section: Introductionmentioning

confidence: 99%

“…Substituting each group of (84)-(99) into nonlinear equation of motion (8) and keeping the terms ∼ β m β m ′ , one can check that Eq.…”

mentioning

confidence: 99%

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Perturbations against a Q-ball. II. Contribution of nonoscillation modes

Smolyakov

2019

Phys. Rev. D

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In the present paper, discussion of perturbations against a Q-ball solution is continued. It is shown that in order to correctly describe perturbations containing nonoscillation modes, it is also necessary to consider nonlinear equations of motion for the perturbations, like in the case of oscillation modes only. It is also shown that the additivity of the charge and the energy of different modes holds for the most general nonlinear perturbation consisting of oscillation and nonoscillation modes.

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Outline of a Nonlinear, Relativistic Quantum Mechanics of Extended Particles

Mielke

1981

Fortschr. Phys.

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A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton‐type solutions of nonlinear, relativistic wave equations. These droplet‐type waves have a quasi‐objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum‐mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle‐wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum‐theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self‐interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle.

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Stability of charged solitons

Cited by 19 publications

References 4 publications

The Skyrme Model

The Skyrme Model

Perturbations against a Q-ball. II. Contribution of nonoscillation modes

Outline of a Nonlinear, Relativistic Quantum Mechanics of Extended Particles

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