Motivated by recent developments on solvable directed polymer models, we define a 'multi-
layer'extension of the stochastic heat equation involving non-intersecting Brownian motions …

In this paper, analytically investigated is a generalized one-dimensional time-dependent
Schrödinger equation. Using Darboux transformation operator technique, we construct the …

A class of exactly solvable Schrödinger equation with moving boundary condition -
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We construct higher-order Darboux transformations for the two-dimensional massless Dirac
equation at zero energy. Both standard and confluent transformations are applicable. Our …

The formalism of Darboux transformations is established for time-dependent Schrödinger
equations with an effective (position-dependent) mass. Explicit formulas are obtained for the …

We construct Darboux transformations of arbitrary order for a generalized, linear, time-
dependent Schrödinger equation, special cases of which correspond to time-dependent …

We extend the formalism of nth order Darboux transformations to the time-dependent
nonhomogeneous Burgers equation (NBE) in (1+ 1) dimensions. Similar to the Schrödinger …

We derive a trace formula for Green's functions of position-dependent (effective) mass
Schrödinger equations that are defined on a real, finite interval and connected by a Darboux …

We study space-time transformations of the time-dependent Schrödinger equation (TDSE)
with time-and position-dependent (effective) mass. We obtain the most general space-time …

Abstract The authors Song and Klauder (2003 J. Phys. A: Math. Gen. 36 8673–84) present a
generalized Darboux transformation, applicable to Hamiltonians with linear terms in the …