The determinant representation of the n-fold Darboux transformation of the Hirota equation
is given. Based on our analysis, the 1-soliton, 2-soliton, and breathers solutions are given …

Soliton interactions occur when two solitons are close enough. In general, periodic
oscillations can be presented during soliton interactions. The periodic oscillations will lead …

In this paper, the analytic three-soliton solution for a high-order nonlinear Schrödinger
equation is obtained by the Hirota's bilinear method. The transmission characteristics of …

Higher-order and multicomponent generalizations of the nonlinear Schrödinger equation
are important in various applications, eg, in optics. One of these equations, the integrable …

In this paper, we study the integrability and exact bright soliton solutions to the coupled
nonlinear Schrödinger equation with higher-order effects arising from nonlinear fiber …

We investigate the modulational instability (MI) of a continuous wave (cw) under the
combined effects of higher-order dispersions, self steepening and self-frequency shift, cubic …

Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear
Schrödinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical …

Based on the Darboux transformation and N-soliton solutions, we obtain the explicit
formulas of arbitrary-order multi-pole (MP) solutions of the Hirota equation via some limit …

We investigate the generalized higher-order nonlinear Schrödinger equation with variable
coefficients under two sets of parametric conditions. The exact one-soliton solution is …

By using Hirota's bilinear method and symbolic computation, solutions for a variable-
coefficient nonlinear Schrödinger equation are obtained theoretically. It is found that the type …