Interaction of coupled higher order nonlinear Schrödinger equation solitons

Borah, Abhijit; Ghosh, Sasanka; Nandy, Sudipta

doi:10.1140/epjb/e2002-00290-x

Cited by 12 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We conclude that, in the J -soliton case, the phase shifts between the limits as t → ±∞, including the shifts in polarization, are independent of the order in which the solitons interact (see also [13]). We note that this result is obtained in [18] by a completely different argument and was also partially addressed in [15,19,20].…”

Section: Multiple Soliton Collisions and Order Independencementioning

confidence: 56%

Soliton interactions in the vector NLS equation

2004

View full text Add to dashboard Cite

Collisions of solitons for two coupled and N-coupled NLS equation are investigated from various viewpoints. By suitably employing Manakov's well-known formulae for the polarization shift of interacting vector solitons, it is shown that the multisoliton interaction process is pairwise and the net result of the interaction is independent of the order in which such collisions occur. Further, this is shown to be related to the fact that the map determining the interaction of two solitons with nontrivial internal degrees of freedom (e.g. vector solitons) satisfies the Yang-Baxter relation. The associated matrix factorization problem is discussed in detail. Soliton interactions are also described in terms of linear fractional transformations, and the problem of existence of a solution for a basic three-collision gate, which has recently been introduced, is analysed.

show abstract

Section: Multiple Soliton Collisions and Order Independencementioning

confidence: 56%

Soliton interactions in the vector NLS equation

2004

View full text Add to dashboard Cite

show abstract

“…Note that the bright N-soliton solutions in (21) are more general than those obtained in [23 -25] because they contain the (m + 1)N complex parameters. We have also analyzed some algebraic properties of the (m +1)-component Wronskians in (16) and (17), and derived the asymptotic formulae in (26) of (21) as Z → ∓∞ for any given set of spectral parameters {λ k } N k=1 . Furthermore, we have revealed some properties for the twoand three-soliton collisions, including the asymptotic patterns of (21) with N = 2 and 3 (see Tables 1 and 2), parametric conditions in (28) and (32) for the preservation of all soliton components in the collision, phaseshift formulae in (29), (33), and (34) induced by the vector-soliton collisions, and generalized LFTs in (30), (35)- (37) for directly describing the state changes undergone by the colliding vector solitons.…”

Section: Discussionmentioning

confidence: 99%

“…For the two-soliton collisions described by (21) with N = 2, we can employ (26) to derive two different asymptotic expressions for the nth colliding soliton (n = 1, 2) as follows: (27) with…”

Section: Two-soliton Collisionsmentioning

confidence: 99%

“…For the three-soliton collisions described by (21) with N = 3, we use (26) to find that the nth colliding soliton (1 ≤ n ≤ 3) has four different asymptotic expressions as follows:…”

Section: Three-soliton Collisionsmentioning

confidence: 99%

“…From the perspective of the inverse scattering transform, [26] has reported the 'inelastic' 1 two-and three-soliton collisions occurring in (2). However, some problems have still not been uncovered for the soliton solutions to (2): (i) What is the determinant representation of the general bright N-soliton solutions?…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bright N-Soliton Solutions to the Vector Hirota Equation from Nonlinear Optics with Symbolic Computation

Tian

2012

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

Under investigation in this paper is the vector Hirota (VH) equation which governs the simultaneous propagation of multiple interacting femtosecond pulses in a certain type of coupled optical waveguides. By the Nth iterated Darboux transformation starting from the zero potential, the VH equation is found to admit the bright N-soliton solutions in terms of the multi-component Wronskian. Asymptotic formulae of the bright N-soliton solutions are derived for any given set of spectral parameters, which allows us to directly analyze the collision dynamics of VH solitons. Via symbolic computation, some collision properties possessed by the two-and three-soliton solutions are revealed from four aspects: the asymptotic patterns of the colliding solitons, parametric conditions for the amplitude-preserving collisions, phase shifts induced by the vector-soliton collisions, and soliton state changes described by the generalized linear fractional transformations.

show abstract

Nonphysicians' and physicians' knowledge and care preferences for Parkinson's disease

Swarztrauber

Graf

2007

Movement Disorders

View full text Add to dashboard Cite

We compared nonphysician and physician health care providers' knowledge of the pharmacological management of Parkinson's disease (PD) and their preferences for referring PD patients to specialists. A survey instrument was mailed in 2003 to all geriatric, neurology, mental health, and primary care physicians, nurse practitioners, and physician assistants in the Pacific Northwest Veterans Health Administration (n = 503). The instrument contained questions about recommended practices for the pharmacotherapy of PD and two clinical scenarios followed by questions regarding referral preferences. The overall response rate was 74%. Nonphysicians answered 46% and physicians answered 50% of questions about PD pharmacotherapy in agreement with recommended clinical practice (P = 0.14). Nonphysician and physician providers did not differ in their preference to refer a PD patient to a specialist for management, but nonphysician providers were more likely to refer a patient to a specialist for diagnostic confirmation odds ratio: 3.03; 95% confidence interval: 1.67, 5.51). Given trends for more nonphysician provider autonomy in patient care, it is reassuring that nonphysician providers have similar knowledge of PD pharmacotherapy as physicians. Policies to substitute nonphysician providers for physician providers may increase referrals to specialty providers for diagnostic confirmation.

show abstract

Interaction of coupled higher order nonlinear Schrödinger equation solitons

Cited by 12 publications

References 7 publications

Soliton interactions in the vector NLS equation

Soliton interactions in the vector NLS equation

Bright N-Soliton Solutions to the Vector Hirota Equation from Nonlinear Optics with Symbolic Computation

Nonphysicians' and physicians' knowledge and care preferences for Parkinson's disease

Contact Info

Product

Resources

About