Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

• DOI: 10.1063/1.4900895
• Publication Date: 2014-11-08T01:30:55Z
• Authors: A. Ganguly; A. Das
• Keywords: Operator (biology); Position (finance)

We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the Schrödinger operator other time-evolution of wave functions. obtain an infinite number conserved quantities for generated nonlinear explicitly show that new KdV is integrable system. Inverse scattering transform method applied to general solution equation, then N-soliton derived reflectionless potentials. Finally, special choice has been made variable function get mass-deformed soliton solution. The influence position time-dependence also different representations kinetic energy on nature such solitons investigated detail. remarkable features are demonstrated several interesting figures contrasted with conventional KdV-soliton associated constant-mass model.