A. Mahalingam

Nonlinear tunneling of nonautonomous optical solitons in combined nonlinear Schrödinger and Maxwell–Bloch systems

We consider the nonlinear Schrodinger–Maxwell–Bloch (NLS–MB) equation with variable coefficients. We construct the Lax pair for the NLS–MB system through AKNS formalism. We derived the two-soliton solution using the Darboux transformation. Finally we demonstrate the nonlinear tunneling of two solitons through dispersion and the nonlinear barrier or well. Our result shows that solitons can be compressed through the tunneling barrier or well with exponential decay for the special choice of variable coefficients.

Multi-soliton propagation in a generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with loss/gain driven by an external potential

In this paper, we introduce a system of the nonlinear Schrodinger-Maxwell-Bloch equation with variable coefficients which represents the propagation of optical pulses in an inhomogeneous erbium doped fiber with loss/gain driven by an external potential. The one and two soliton solutions in explicit forms are generated by using the Darboux transformation and the associated Lax pair. We consider the distributed amplification system, and some main features of the solutions are demonstrated graphically. We also consider the concept of soliton propagation in a dispersion managed erbium doped fiber and through symbolic computation, we have carried out our study from an analytic viewpoint.

Propagation of dispersion–nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

In this paper, a generalized nonlinear Schrodinger–Maxwell–Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Backlund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed.

Integrability aspects of NLS–MB system with variable dispersion and nonlinear effects

Abstract In this paper, we analyze the integrability aspects of the NLS–MB system with variable dispersion and nonlinear effects. We obtain the constraints for which the above system becomes integrable by using the Painleve singularity analysis. Obtained results are in agreement with the known results.

Propagation of dark solitons in a system of coupled higher-order nonlinear Schrödinger equations

In this paper, we consider the higher-order linear and nonlinear effects in optics and analyse a coupled system of higher-order nonlinear Schrodinger equations to identify the conditions for dark-soliton propagation through Painleve analysis, to supplement the known bright-soliton conditions. We also construct the explicit Lax pair and the Hirota bilinear form is used to generate one and two dark solitons.

Hidden possibilities in soliton switching through tunneling in erbium doped birefringence fiber with higher order effects

In this paper, coupled higher order nonlinear Schrödinger–Maxwell–Bloch equations are studied for the ultrashort pulse propagation in erbium-doped birefringent fiber system. Lax pair is constructed for the CHNLS–MB system. Through the Darboux method and symbolic computation, analytic two-soliton solution is obtained. To analyze the specific problem, we design an optimal system by properly choosing the special form of variable coefficients. Here, using obtained two-soliton solution, tunneling of femtosecond soliton through barrier and well is investigated. While solitons are passing through barrier and well, some unexpected behavior is observed and hidden possibilities in switching action through tunneling is investigated.

Solitons in the system of coupled Hirota–Maxwell–Bloch equations

Abstract We propose the system of coupled Hirota–Maxwell–Bloch equations which governs the propagation of optical pulses in an erbium doped nonlinear fibre with higher order dispersion, self-steepening and self induced transparency (SIT) effects. The Lax pair is explicitly constructed and the soliton solution is obtained using the Darboux–Backlund transformations. Hence, the system is found to admit soliton type lossless wave propagation.

Complete integrability of N-coupled higher-order nonlinear Schrödinger equations in nonlinear optics

The coupled higher-order nonlinear Schrodinger equations are generalized to an N-coupled system which governs the propagation of N fields in a fibre with all the higher-order effects like third-order dispersion, Kerr dispersion and stimulated Raman scattering. The explicit Lax pair is constructed and the soliton solutions are obtained using the Darboux-Backlund transformation. Finally, the Hirota bilinear form for the N-coupled system equations is also presented.

Application of Painlevè analysis to the wave-wave scattering problem in a two-level resonant medium

In this paper, we apply the Painleve singularity structure analysis to the wave-wave scattering problem which manifests itself in nonlinear optics as the stimulated Raman scattering (SRS) and self-induced transparency (SIT) and in plasma physics as the interaction of electromagnetic waves with the ion-acoustic waves. The governing equations are expected to be integrable from the point of view of Painleve (P) analysis.