Soliton solutions to a reverse-time non-local nonlinear Schrödinger differential equation

Under vanishing and non-vanishing boundary conditions, we consider general soliton solutions of a fully PT-symmetric multidimensional non-local nonlinear Schrödinger equation with time reversal. Concrete expressions could be written as N × N Gram-type determinants by employing Hirota's bilinearity and the KP hierarchy reduction, for positive integer N . Furthermore, the typical dynamics and behaviours of high-order soliton solutions are illustrated graphically. (author)