Solitons In Presence Research Articles

A Fractional Model to Study Soliton in Presence of Charged Space Debris at Low-Earth Orbital Plasma Region

A Fractional Model to Study Soliton in Presence of Charged Space Debris at Low-Earth Orbital Plasma Region

Extraction of new optical solitons in presence of fourth-order dispersion and cubic-quintic nonlinearity

Extraction of new optical solitons in presence of fourth-order dispersion and cubic-quintic nonlinearity

Pure-quartic solitons in presence of weak nonlocality

In this paper, we study the characteristics of pure-quartic optical solitons in a nonlinear medium having a weakly nonlocal response. We propose an nonlinear Schrödinger equation incorporating pure fourth-order diffraction, Kerr nonlinearity and weak nonlocality to describe the transmission of solitons in the system. We obtain analytic pure-quartic soliton solutions to this model in a variety of shapes and forms, unlike the case of the model without taking into account the weak nonlocal contribution. Besides, we find that the obtained localized structures have both bright and dark type waveforms in the transmission system. Interestingly, the functional forms of these solitons are expressed in terms of sech and tanh functions which do not possess oscillating tails, markedly different from the conventional pure-quartic solitons in the absence of weak nonlocality. These structures exist for both positive and negative quartic diffraction coefficient whereas pure-quartic solitons in the absence of nonlocality occur only for negative fourth-order dispersion. The numerical examples are presented for illustrating the soliton evolution dynamics in the optical waveguide.

Highly dispersive optical solitons and conservation laws with Kudryashov’s sextic power-law of nonlinear refractive index

This current work addresses highly dispersive solitons in presence of Kudryashov’s sextic power law. Three independent approaches have made this retrieval possible. However, it is only with specific value of the power-law nonlinearity parameter, bright solitons emerge. Finally, conservation laws are presented for the model.

Cubic–quartic optical solitons with Kudryashov's arbitrary form of nonlinear refractive index

The focus of attention in this paper is to retrieve cubic–quartic solitons in presence of Kudryashov's law including generalized non-local law. The two integration approaches are also due to Kudryashov. A range of soliton solutions have been recovered in the work.

Dark-bright soliton interactions in coupled nonautonomous nonlinear Schrödinger equation with complex potentials

We investigate dark-bright soliton dynamics in a coupled nonlinear Schrödinger equation in presence of complex potentials and the associated spectral problem. Using asymptotic analysis and graphical analysis, we study the interactions of soliton complexes under different potentials. We present the results of elastic and inelastic interaction between solitons in presence of the potentials. The external potential brings about notable changes in the dynamics of soliton by changing it’s velocity, frequency and the wave number. The changes are however, same on the all the solitons and hence the external potential do not alters the conditions of the elastic interaction. We also present interesting features of complex three soliton interactions under the complex potentials. The shape change may occur even when there is no relative velocity between solitons. We hope that the present analysis would be useful for a better understanding of soliton interactions in an inhomogeneous nonlinear fiber and the dynamics of condensates in atomic physics.

Cubic-quartic optical soliton perturbation by semi-inverse variational principle

This paper secures bright optical solitons in presence of third and fourth order dispersion terms while group velocity dispersion term is absent. The perturbation terms that are included appear with full nonlinearity. The semi-inverse variational principle is implemented to secure such solutions.

Optical solitons in presence of higher order dispersions and absence of self-phase modulation

This paper proposes a new model for soliton transmission through optical fibers where self-phase modulation is negligibly small and hence removed. The model however includes spatio-temporal dispersions, of second and third order, to compensate for low group velocity dispersion. The balance for sustaining solitons is provided by nonlinear dispersion terms that are considered in this model.

Stability of solitary waves in random nonlocal nonlinear media

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane, by means of both numerical simulations and analytical estimates. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on the evolution of the Hamiltonian of the soliton and its power. The first criterion allows us to estimate a time (or distance) over which the soliton preserves its form. The second criterion gives the life-time of the solitary wave packet in terms of its radiative power losses. We derive a simplified mean field approach which allows us to calculate the power loss analytically in the physically relevant case of weakly correlated noise, which in turn serves as a lower estimate of the life-time for correlated noise in general case.

Optical solitons in presence of higher-order effects

In this paper, we seek special soliton solutions of so-called Higher-Order Nonlinear Schroedinger Equation, which describes the propagation of light waves in nonlinear optical media. Using a developed Jacobi elliptic function expansion method described in [8], we show that in the case of four-order dispersion these traveling wave solutions do not exist. As a byproduct, we regain the results obtained by other authors [8, 9] for the case when only the dispersion to the third order is taken into account. Full Text: PDF References C. Long Van, M. Trippenbach, "New Optical Solitary waves in the higher order nonlinear Schroedinger Equation", Scientific Bulletin 126, Technical University of Zielona Gora, Poland 2001, p.19 (Cao Long Van ed.). V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan,"Propagation Technique for Ultrashort Pulses I", Computational Methods in Science and Technology 14(1), 5 (2008) V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan,"Propagation Technique for Ultrashort Pulses II ", Computational Methods in Science and Technology 14(1), 13 (2008) V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan,"Propagation Technique for Ultrashort Pulses III ", Computational Methods in Science and Technology 14(1), 21 (2008) C. Long Van, P. P. Goldstein, "A concise Course in nonlinear Partial Differential Equations" (University of Zielona Gora 2008). A. V. Buryak and Yu. S. Kivshar,"Solitons due to second harmonic generation", Phys. Lett. A 197, 407 (1995) [CrossRef] M. Trippenbach, M. Matuszeski, E. Infreld, Cao Long Van, R. S. Tasgal, J. B. Band,"Enhancement of third harmonic generation by wave vector mismatch to counter phase- modulation ", Optics Comm. 229, 391 (2004) [CrossRef] S. A. El-Wakil, M.A. Abdou, A. Elhanbaly,"New solitons and periodic wave solutions for nonlinear evolution equations", Phys. Lett. A 353, 40 (2006) [CrossRef] Q. Yang, C.Q. Dai, J. F. Zhang,"Higher-Order Effects Induced Optical Solitons in Fiber", International Journal of Theoretical Physics 44, 1117 (2005) [CrossRef]

Perturbation of topological solitons due to sine-Gordon equation and its type

This paper studies the adiabatic dynamics of topological solitons in presence of perturbation terms. The solitons due to sine-Gordon equation, double sine-Gordon equation, sine–cosine Gordon equation and double sine–cosine Gordon equations are studied, in this paper. The adiabatic variation of soliton velocity is obtained in this paper by soliton perturbation theory.

Soliton Perturbation Theory for the Compound KdV Equation

The soliton perturbation theory is used to study the solitons that are governed by the compound Korteweg de-Vries equation in presence of perturbation terms. The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained.

Soliton perturbation theory for the modified nonlinear Schrödinger’s equation

The soliton perturbation theory is used to study the solitons that are governed by the modified nonlinear Schrödinger’s equation. The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained. In particular, the nonlinear gain (damping) and filters or the coefficient of finite conductivity are treated as perturbation terms for the solitons.

Soliton perturbation theory for Alfvén waves in plasmas

The soliton perturbation theory is used to study the Alfvén waves in plasmas that are governed by the derivative nonlinear Schrödinger’s equation. The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained. In particular, the nonlinear gain (damping) and the coefficient of finite conductivity are treated as perturbation terms.

PERTURBATIONS OF DISPERSION-MANAGED OPTICAL SOLITONS

This paper studies the propagation of solitons through an optical fiber, with strong dispersion-management in presence of perturbation terms. The adiabatic parameter dynamics of the solitons in presence of such perturbation terms have been obtained by using the variational principle. In particular, the Gaussian and super-Gaussian pulses have been considered.

Theory of non-Kerr law solitons

This paper is a theoretical study of solitons governed by the nonlinear Schrödinger's equation (NLSE) with non-Kerr law nonlinearity. The soliton perturbation theory is used to obtain the parameter dynamics of solitons that are governed by this equation. This study is extended to the case of the vector NLSE and its further generalization. In addition, we have studied the adiabatic parameter dynamics of solitons in presence of perturbation terms.

INTEGRO-DIFFERENTIAL PERTURBATIONS OF DISPERSION-MANAGED SOLITONS

This paper studies the propagation of solitons through an optical fiber, with strong dispersion-management, in presence of integro-differential type perturbations including the nonlinear damping. The parameter dynamics of the solitons in presence of such perturbation terms have been obtained. In particular, the Gaussian and super-Gaussian pulses have been considered.

Dynamics of optical solitons with dispersion-management

The variational principle is employed to study chirped solitons that propagate through optical fibers and is governed by the dispersion-managed nonlinear Schrödinger's equation. Here, in this paper, we have considered both kinds of fibers namely polarization preserving and birefringent type. The study is extended to obtain the adiabatic evolution of the parameters of such solitons in presence of perturbation terms for both types of fibers.

DYNAMICS OF SUPER-GAUSSIAN SOLITONS IN BIREFRINGENT OPTICAL FIBERS

The variational principle is employed to obtain the parameter dynamics of a super-Gaussian chirped soliton that propagates through birefringent optical fibers and is governed by the dispersion-managed vector nonlinear Schrödinger's equation. The waveform deviates from that of a classical soliton. The periodically changing strong chirp of such a soliton reduces the effective nonlinearity that is necessary for balancing the local dispersion. This study is extended to obtain the adiabatic evolution of the parameters of such a soliton in presence of perturbation terms.

Dynamics of Gaussian and Super-Gaussian Solitons in Birefringent Optical Fibers

The variational principle is employed to obtain the parameters dynamics of Gaussian and super-Gaussian chirped solitons which propagates through birefringent optical fibers that is governed by the dispersion-managed vector nonlinear Schrodinger's equation. The waveform deviates from that of a classical soliton. The periodically changing strong chirp of such a soliton reduces the effective nonlinearity that is necessary for balancing the local dispersion. This study is extended to obtain the adiabatic evolution of the parameters of such a soliton in presence of perturbation terms.