My broad research area is Applied Mathematics. Speciazlized area includes Quantum Mechanics (Hermitian & Non-Hermitian) and Nonlinear Dynamics. In the first field, I work in 1D stationary Schroedinger Equation for ES and QES potentials in the framework of supersymmetry and Lie-algebraic approach. In the 2nd field, my interest is in the solution (general and soliton) of evolution equation and in stability analysis of the soution in the context of dynamical theory. Quantum computaion, Fluid mechanics (classical & quantum), Nonlinear Optics, QED, QCD, QFT etc also draw my interest.
I have discovered algebraization of Associated Lame Equation in 2000, new Shape-invariant potentials in PDM QM through 1st & 2nd order SUSY in 2007, modelled a nanoscal heterojunction by Morse-type potential having delta-singularity and solved it through SUSY transformation in 2009, solved CPT-conserved effective mass models for N-th order differential representation of charge operator in 2010. These are some of my achievements in QM.
In the field of Nonlinear Dynamics, I have found a new generalized KdV equation in connection with PDM QM, and have sucessfully obtained most general solution including soliton through Inverse Scattering Transform in 2015, obtained travelling wave solution of Nonlinear Schrodinger equation and various other nonlinear equation during 2012-2015, made a stability analysis of TWS of generalized KP-type euation with or without viscous term in 2014 etc.
Recent works include investigation of new Hermitian & non-Hermitian potentials, periodic potentials & crystal structure etc in QM, Entanglement and Quantum Gates in Quantum Computation, complex NLSE, matrix & discrete nonlinear equations in Nonlinear Dynamics etc. ,