Collision of N-solitons in a fifth-order nonlinear Schrödinger equation

The existence of N-solitons in a fifth-order nonlinear quintic Schrödinger equation is investigated through the use of a Hirota's differential operator, which utilizes only one auxiliary function. This minimal use of auxiliary functions is a novel modification of the bilinear forms that allow us to obtain a larger and a more general class of N-solitons. As the number of auxiliary functions increases, the obtained solutions are more restricted and may not exhibit some of the important behaviors, thus the novel solutions given here are more general. Several classes of 4-solitons exhibiting elastic collisions, and non-elastic collisions that lead to the gain and the loss of amplitudes after collision in a conservative system are presented. Various plots to support the analytic results are presented with propagations illustrated along the x-axis. The explicit expressions for the solitons turn out to be the same as those given by Hirota for the third-order case, but the dispersion relation is different.