Wave Systems with an Infinite Number of Localized Traveling Waves

Alfimov, G. L.; Medvedeva, E. V.; Pelinovsky, Dmitry E.

doi:10.1103/physrevlett.112.054103

Cited by 40 publications

(43 citation statements)

References 32 publications

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“…Rigorous analysis of these solutions in various systems can be found in [36][37][38]. In a recent work [39] authors have analyzed a general class of dispersive nonlinear systems and formulated sufficient conditions for the existence of a countable infinity of single humped, embedded solitons.…”

Section: Introductionmentioning

confidence: 99%

Solitary waves in diatomic chains

et al. 2016

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We consider the mechanism of formation of isolated localized wave structures in the diatomic Fermi-Pasta-Ulam (FPU) model. Using a singular multiscale asymptotic analysis in the limit of high mass mismatch between the alternating elements, we obtain the typical slow-fast time scale separation and formulate the Fredholm orthogonality condition approximating a sequence of mass ratios supporting the formation of solitary waves in the general type of diatomic FPU models. This condition is made explicit in the case of diatomic Toda lattice. Results of numerical integration of the full diatomic Toda lattice equations confirm the formation of these genuinely localized wave structures at special values of the mass ratio that are close to the analytical predictions when the ratio is sufficiently small.

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Section: Introductionmentioning

confidence: 99%

Solitary waves in diatomic chains

et al. 2016

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“…It is worth noting that transitional radiation in an optical lattice may prevent the formation of moving solitons 40 . There are systems where solitons with discrete set of propagation velocities can exist due to complete suppression of transitional radiation 41, 42 . In systems where the dynamics can be approximated by coupled counterpropagating waves (e.g.…”

Section: Introductionmentioning

confidence: 99%

Moving Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity

Chowdhury

Atai

2017

Sci Rep

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The existence, stability and collision dynamics of moving Bragg grating solitons in a semilinear dual-core system where one core has the Kerr nonlinearity and is equipped with a Bragg grating with dispersive reflectivity, and the other core is linear are investigated. It is found that moving soliton solutions exist as a continuous family of solutions in the upper and lower gaps of the system’s linear spectrum. The stability of the moving solitons are investigated by means of systematic numerical stability analysis, and the effect and interplay of various parameters on soliton stability are analyzed. We have also systematically investigated the characteristics of collisions of counter-propagating solitons. In-phase collisions can lead to a variety of outcomes such as passage of solitons through each other with increased, reduced or unchanged velocities, asymmetric separation of solitons, merger of solitons into a quiescent one, formation of three solitons (one quiescent and two moving ones) and destruction of both solitons. The outcome regions of in-phase collisions are identified in the plane of dispersive reflectivity versus frequency. The effects of coupling coefficient, relative group velocity in the linear core, soliton velocity and dispersive reflectivity and the initial phase difference on the outcomes of collisions are studied.

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“…After substituting the ansatz (6) into Eq. (5) Currently it is a well-established fact [10][11][12][13][14][18][19][20] that for the discrete Klein-Gordon equations of the type (3), the continuous family of moving solitons turns into the discrete finite set of monotonic …”

Section: Soliton Mobility In the Hamiltonian Limitmentioning

confidence: 99%

“…If the inductive coupling between the junctions is small, the free fluxon motion becomes impossible. However, the possibility of radiationless propagation of solitary waves in discrete media for selected values of velocity has been reported in the number of papers [10][11][12][13][14][15][16][17][18][19][20]. Also, free propagation of the bound states of several discrete topological solitons has been reported by Peyrard and Kruskal more than 30 years ago [8].…”

Section: Introductionmentioning

confidence: 98%

Embedded soliton dynamics in the asymmetric array of Josephson junctions

Starodub

Zolotaryuk

2017

Low Temperature Physics

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The dc-biased annular array of three-junction asymmetric superconducting quantum interference devices (SQUIDs) is investigated. The existence of embedded solitons (solitons that exist despite the resonance with the linear waves) is demonstrated both in the unbiased Hamiltonian limit and in the dc-biased and damped case on the current-voltage characteristics (CVCs) of the array. The existence diagram on the parameter plane is constructed. The signatures of the embedded solitons manifest themselves as inaccessible voltage intervals on the CVCs. The upper boundary of these intervals is proportional to the embedded soliton velocity.

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Wave Systems with an Infinite Number of Localized Traveling Waves

Cited by 40 publications

References 32 publications

Solitary waves in diatomic chains

Solitary waves in diatomic chains

Moving Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity

Embedded soliton dynamics in the asymmetric array of Josephson junctions

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