Schrödinger equation with time-dependent mass function and associated generalized KdV equation

摘要: We show that a time-dependent disturbance term could be embedded into Korteweg–de Vries (KdV) equation. This is accomplished through Lax pair formulation of linearized scattering problem corresponding to the Schrodinger A new generalized KdV equation obtained by considering mass function. Choosing initial data for stationary potential, we solve direct problem. Then, in inverse problem, Gel'fand–Levitan integral solved derive solution our Finally, an elliptic functional form chosen function obtain soliton solution.