Bright and dark soliton solutions to coupled nonlinear Schrodinger equations

Radhakrishnan, R.; Lakshmanan, M.

doi:10.1088/0305-4470/28/9/025

Cited by 253 publications

(186 citation statements)

References 14 publications

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“…(9)- (10) and (5)- (6), corresponding to the ground and excited states in the linear limit for component f + , emerge (bifurcate) at some critical values of D with the corresponding eigenvalues µ + of the linear problem based on Eq. (13). These values are found below by performing numerical continuations over the aforementioned parameters.…”

Section: The Model and Analytical Considerationsmentioning

confidence: 99%

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

et al. 2016

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We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self-and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multi-ring complexes into stable VB solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self-and cross-repulsive nonlinearities.

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Section: The Model and Analytical Considerationsmentioning

confidence: 99%

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

et al. 2016

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“…A detailed investigation on the soliton solutions of two coupled NLS equation with same nonlinearity (nonlinear coefficients have the same signs '+' and '-') and mixed nonlinearity (nonlinear coefficients have opposite signs) gave birth to three different vector soliton solutions, namely (i) bright-bright [33,34], (ii) bright-dark [56,57] and (iii) dark-dark solitons [34,58]. The explicit multi-bright and multi-dark soliton solutions of the Manakov system were obtained in [34,35]. Recently, one dark-dark soliton and the general breather solution of a generalized version of Eq.…”

Section: Model and Rw Solutions Of Two-dimensional Two Coupled Vcnls mentioning

confidence: 99%

“…The vector NLS equations yield potentially rich and significant results for optical fiber communication systems [12]. Motivated by this, several studies have also been undertaken to identify the localized solutions in coupled NLS equations with constant coefficients [33,34,35,36,37,38,39,40,41,42,43]. Subsequently attempts have been made to identify the localized solutions such as bright-bright, bright-dark, dark-dark soliton and RW solutions in the coupled vcNLS equations (in one-dimensions) [44,45,46,47,48,49,50,51].…”

Section: Introductionmentioning

confidence: 99%

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

2016

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Abstract. We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.

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“…A principal paradigm consists of the dark-bright (DB) solitary wave and related structures such as dark-dark solitary waves that have long been studied theoretically [3][4][5][6][7][8][9]. The experimental study of such states was pioneered much earlier in nonlinear optics, including e.g.…”

Section: Introductionmentioning

confidence: 99%

Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates

et al. 2016

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Multi-component Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures.In recent theoretical work, the notion of magnetic solitons has been introduced. Here we generalize this concept to vector dark-antidark solitary waves in multi-component Bose-Einstein condensates.We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and inter-component repulsion. Armed with this more general conceptual framework, we expand the notion of such states to higher dimensions presenting the possibility of both vortex-antidark states and ring-antidark-ring (dark soliton) states. We perform numerical continuation studies, investigate the existence of these states and examine their stability using the method of Bogolyubovde Gennes analysis. Dark-antidark and vortex-antidark states are found to be stable for broad parametric regimes. In the case of ring dark solitons, where the single-component ring state is known to be unstable, the vector entity appears to bear a progressively more and more stabilizing role as the inter-component coupling is increased.

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Bright and dark soliton solutions to coupled nonlinear Schrodinger equations

Cited by 253 publications

References 14 publications

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates

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