R. Radha

Periodic and localized solutions of the long wave-short wave resonance interaction equation

In this paper, we investigate the (2+1)-dimensional long wave–short wave resonance interaction (LSRI) equation and show that it possess the Painleve property. We then solve the LSRI equation using Painleve truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions, such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.

Phase Engineering and Solitons of Bose–Einstein Condensates with Two- and Three-Body Interactions

We introduce a phase imprint into the macroscopic order parameter governing the dynamics of Bose–Einstein condensates with attractive two-body interactions described by a cubic Gross–Pitaevskii (GP) equation and then engineer the imprinted phase suitably to generate the modified GP equation. The modified GP equation describes the dynamics of condensates with both two- (attractive) and three-body (attractive and repulsive) interactions in an expulsive harmonic trap. Employing gauge transformation approach, we then construct bright solitons of the modified GP equation. We observe that the attractive three-body interactions introduce an additional nontrivial phase in the matter wave solitons arising due to attractive two-body interactions without changing their density while the repulsive three-body interactions enormously increase the density of the condensates without causing any change in the phase of the solitons originating from attractive two-body interactions.

Rotation of the trajectories of bright solitons and realignment of intensity distribution in the coupled nonlinear Schrödinger equation.

We revisit the collisional dynamics of bright solitons in the coupled Nonlinear Schrödinger equation. We observe that apart from the intensity redistribution in the interaction of bright solitons, one also witnesses a rotation of the trajectories of bright solitons . The angle of rotation can be varied by suitably manipulating the Self-Phase Modulation (SPM) or Cross Phase Modulation (XPM) parameters.The rotation of the trajectories of the bright solitons arises due to the excess energy that is injected into the dynamical system through SPM or XPM. This extra energy not only contributes to the rotation of the trajectories, but also to the realignment of intensity distribution between the two modes. We also notice that the angular separation between the bright solitons can also manouvred suitably. The above results which exclude quantum superposition for the field vectors may have wider ramifications in nonlinear optics, Bose-Einstein condensates, Left Handed (LH) and Right Handed (RH) meta materials.

The collision of multimode dromions and a firewall in the two-component long-wave-short-wave resonance interaction equation

In this communication, we investigate the two-component long-wave‐shortwave resonance interaction equation and show that it admits the Painlev´ e property. We then suitably exploit the recently developed truncated Painlev´ e

Explode-Decay Solitons in the Generalized Inhomogeneous Higher-Order Nonlinear Schrödinger Equations

In this paper we investigate the generalized inhomogeneous higher-order nonlinear Schrödinger equations, generated recently by deforming the inhomogeneous Heisenberg ferromagnetic spin system through a space curve formalism [Phys. Lett. A 352, 64 (2006)] and construct their multisoliton solutions, using gauge transformation. The amplitude of the bright soliton solutions generated grows and decays with time, and there is an exchange of energy between soliton trains during interaction.

Remote controlling the dynamics of Bose-Einstein condensates through time-dependent atomic feeding and trap

In this paper, we generate the Lax pair of the nonconservative Gross?Pitaevskii (GP) equation with time-dependent linear and harmonic oscillator potentials and construct a multisoliton solution using gauge transformation. We show how an interplay between the dispersion coefficient, scattering length and atomic feeding can suitably be exploited to remote control the dynamics of solitons, thereby generating favorable profiles of Bose?Einstein condensates (BECs), notable among them being the matter wave similaritons.

Line-soliton dynamics and stability of Bose–Einstein condensates in (2+1) Gross–Pitaevskii equation

We investigate the (2+1)-dimensional Gross–Pitaevskii equation in an isotropic expulsive harmonic trap and generate bright line solitons for the condensates by employing the Hirota method. We observe that one can increase the density of the condensates (or line solitons) by suitably tuning the trap frequency even for constant scattering lengths. The two line-soliton dynamics indicate the occurrence of an instability in the condensates once the density exceeds a critical value. This instability could possibly be overcome by the addition of suitable dissipation which subsequently increases the lifespan of the condensates.

Interplay Between Dispersion and Nonlinearity in Femtosecond Soliton Management

In this paper, we investigate the inhomogeneous higher-order nonlinear Schr¨odinger (NLS) equation governing the femtosecond optical pulse propagation in inhomogeneous fibers using gauge transformation and generate bright soliton solutions from the associated linear eigenvalue problem. We observe that the amplitude of the bright solitons depends on the group velocity dispersion (GVD) and the self-phase modulation (SPM) while its velocity is dictated by the third-order dispersion (TOD) and GVD. We have shown how the interplay between GVD, SPM, and TOD can be profitably exploited to change soliton width, amplitude (intensity), shape, phase, velocity, and energy for an effective femtosecond soliton management. The highlight of our paper is the identification of ‘optical similaritons’ arising by virtue of higher-order effects in the femtosecond regime.

Truncated Painlevé Expansion – A Unified Approach to Exact Solutions and Dromion Interactions of (2+1)-Dimensional Nonlinear Systems

In this paper, we formulate a method wherein we harness the results of the Painlevé analysis to generate the solutions of the (2+1)-dimensional Ablowitz-Kaup-Newell-Segur system completely in terms of the arbitrary functions. This method is mainly based on the results of the truncated Painlevé expansion. Different types of interactions among dromions are deeply understood both analytically and numerically. Especially, different from the traditional viewpoint, we point out that the soliton (dromion) fission and fusion may be an approximate phenomenon.

Digging into the Elusive Localised Solutions of (2+1) Dimensional sine-Gordon Equation

Abstract In this paper, we revisit the (2+1) dimensional sine-Gordon equation analysed earlier [R. Radha and M. Lakshmanan, J. Phys. A Math. Gen. 29, 1551 (1996)] employing the Truncated Painlevé Approach. We then generate the solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the closed form of the solution, we have constructed dromion solutions and studied their collisional dynamics. We have also constructed dromion pairs and shown that the dynamics of the dromion pairs can be turned ON or OFF desirably. In addition, we have also shown that the orientation of the dromion pairs can be changed. Apart from the above classes of solutions, we have also generated compactons, rogue waves and lumps and studied their dynamics.