My broad research area is Applied Mathematics. Sub-areas are Differential Equation (ODE & PDE), Diffrence Equation, Wave Mechanics, Matrix Mechanics, Fluid Mechanics, Lie-algebraic theory etc. 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. ,
Associated Lame and various other new classes of elliptic potentials from sl(2,R) and related orthogonal polynomials by Ganguly A. Journal of Mathematical Physics 43 1980-1989 (2002)
New classes of quasi-solvable potentials, their exactly solvable limit and related orthogonal polynomials by Ganguly A. Journal of Mathematical Physics 43 5310-5324 (2002)
Associated Lame Equation, Periodic Potentials & SL(2,R) by Ganguly A. Modern Physics Letters A 15 1923-1930 (2000)
Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry by Ganguly A., Nieto L. M. Journal of Physics A 40 7265-7281 (2007)
Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform by Ganguly A., Das A. Journal of Mathematical Physics 55 1121021-11210220 (2014)
A new effective mass Hamiltonian and Associated Lame equation: Bound States by Ganguly A., Ioffe M. V., Nieto L. M. Journal of Physics A 39 14659-14680 (2006)
Explicit solutions and stability analysis of the (2+1) dimensional KP-BBM equation with dispersion effect by Ganguly A., Das A. Communications in Nonlinear Science and Numerical Simulations 25 102-117 (2015)
Exactly solvable Associated Lame potentials and Supersymmetric Transformations by Fernandez D. J., Ganguly A. Annals of Physics 322 1143-1161 (2007)
Supersymmetry across nanoscale heterojunctions by Bagchi B., Ganguly A. , Sinha A. Physics Letters A 374 2397-2400 (2010)
New Supersymmetric Partners for the Associated Lame Potentials by Fernandez D. J., Ganguly A. Physics Letters A 338 203-208 (2005)
Area of Research: Analytical & Numerical study of DE and their applications