Resonance- and phase-induced window sequences in vector-soliton collisions

Tan, Yi; Yang, Jianke

doi:10.1016/s0375-9601(01)00564-3

Cited by 5 publications

(7 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tan and Yang numerically studied the interaction of two solitons initialized in orthogonal channels with identical amplitude, headed toward each other with exactly opposite initial velocities [15,16,17]. For small values of β ≈ 0.05, their simulations show that waves traveling above a critical velocity v c , the solitons pass by each other, losing a little bit of speed, but not otherwise showing a complicated interaction.…”

Section: Physical Problem and Prior Resultsmentioning

confidence: 99%

“…This relation is used to estimate the resonant initial velocities. This reasoning has subsequently been adapted in studies of sine-Gordon kink-defect interactions [24,25] and of vector soliton collisions [15,16,17] which are the focus of this paper.…”

Section: Physical Problem and Prior Resultsmentioning

confidence: 99%

“…If V in < V c , then the energy is negative after one pass, and the solitons reverse direction, setting up the second pass. On the first pass, the change of energy was shown in (15) to be negative, but on subsequent passes, it may take either sign, by (17). On the second, and subsequent, passes the solitons may escape if the energy is positive, or may be reversed again.…”

Section: Matched Asymptotic Construction Of Solutions a The Expansion...mentioning

confidence: 99%

“…Solitary wave collisions in non-integrable wave equations, can usually not be found in closed form, and show a much richer variety of behaviors: the waves may attract or repel each other and, upon collision, the solitary waves may lose their coherence and break apart, merge into a single localized structure, or even oscillate about one another. [14,15,16,17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

“…Interspersed among the initial velocities that lead to this capture are "resonance windows", for which the two waves approach each other, interact with each other for a finite time, and then move apart again; see the second and third graph in figure 1. This has been explored by Tan and Yang in a system of coupled nonlinear Schrödinger (CNLS) equations that model nonlinear propagation of light in birefringent optical fibers [15,16,17], and by Cambell and collaborators in kink-antikink interaction in the φ 4 equations and several other nonlinear Klein-Gordon models [18,19,20,21]. These windows form a complicated fractal structure that has been described qualitatively and even quantitatively, but for which the underlying mechanism has been poorly understood.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Vector-soliton collision dynamics in nonlinear optical fibers

Goodman

Haberman

2005

Phys. Rev. E

View full text Add to dashboard Cite

We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schrödinger equations. We study a low-dimensional model system of Hamiltonian ordinary differential equations (ODEs) derived by Ueda and Kath and also studied by Tan and Yang. We derive a further simplified model which has similar dynamics but is more amenable to analysis. Sufficiently fast solitons move by each other without much interaction, but below a critical velocity the solitons may be captured. In certain bands of initial velocities the solitons are initially captured, but separate after passing each other twice, a phenomenon known as the two-bounce or two-pass resonance. We derive an analytic formula for the critical velocity. Using matched asymptotic expansions for separatrix crossing, we determine the location of these "resonance windows." Numerical simulations of the ODE models show they compare quite well with the asymptotic theory.

show abstract

Section: Physical Problem and Prior Resultsmentioning

confidence: 99%

Section: Physical Problem and Prior Resultsmentioning

confidence: 99%

Section: Matched Asymptotic Construction Of Solutions a The Expansion...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Vector-soliton collision dynamics in nonlinear optical fibers

Goodman

Haberman

2005

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

Scattering of Bright Solitons Due to Defects in Binary Bose‐Einstein Condensates with Nonlinear Optical Lattices

Sekh

2024

Annalen der Physik

View full text Add to dashboard Cite

Spatially overlapped coupled matter‐wave bright solitons are considered in binary Bose‐Einstein condensates with nonlinear optical lattices(NOLs) and study the properties of scattering patterns due to a localized defect. It is shown that spatially overlapped solitons become separated and exhibit different scattering patterns with the variation of inter‐species interaction. The NOL interplays with the defect and tends to influence the scattering properties. However, the effect of NOL varies with strength of inter‐component interaction. It is found that, if this interaction is weak then the scattering center gets shifted outside the defect. However, for a stronger inter‐component interaction, the scattering takes place from the defect and leads to different scattering patterns.

show abstract