Research Projects

Nonlinear Schrodinger (NLS) equation is inevitable in theoretical physics as it can be used to define almost all physical phenomena ranging from optics, plasma physics to quantum technologies. In this project, we have considered the generalized inhomogeneous NLS equation which illustrates the dynamics of optical soliton propagation in real-time scenario of the optical fibers/waveguides. In other words, we have also included inhomogeneous nonlinear media, such as dispersion, nonlinearity, linear and harmonic potentials, and gain/loss parameters in the NLS equation which arises due to the intensity dependent refractive index of the fiber/waveguide. Considering the above physically realizable entities along with nonlinear optical media, we are interested to study the bound soliton molecule (two-soliton interactions) solutions/non-degenerate soliton solutions. To investigate the dynamical characteristics of soliton molecule solutions, we take into account three different forms for inhomogeneous media namely (i) exponential, (ii) periodic and (iii) hyperbolic dispersion profiles. We also intend to construct the triplet and quartet soliton molecule solutions/non-degenerate soliton solutions by considering the discrete eigenvalues with same real parts. Our theoretical results will show various interesting features of stable optical soliton molecules, energy-sharing collision between bound soliton molecules and soliton interactions. For example, the intensity of the propagating soliton molecule increases in a controllable manner by choosing exponential / hyperbolic forms of the inhomogeneous media. This result suggests it may be possible to experimentally demonstrate the stable soliton molecule propagation in a controlled fashion using properly engineered optical fiber/waveguides. One can also alternatively increase or decrease the intensity of the stable bound soliton molecules by choosing periodic form for inhomogeneous media. In summary, our results will certainly act as a test ground for localized wave dynamics in various optical experiments and lead to real time applications.