Nth order smooth positon and breather-positon solutions of a generalized nonlinear Schr\"{o}dinger equation

TL;DR

This paper constructs and analyzes higher order smooth positon and breather-positon solutions of a generalized nonlinear Schrödinger equation, revealing how higher order nonlinear effects influence their shape, compression, and dynamics.

Contribution

It introduces a generalized Darboux transformation method to derive Nth order positon and breather-positon solutions, highlighting the impact of higher order nonlinearities.

Findings

Positon solutions become highly compressed due to higher order nonlinear effects.

The direction of positons changes with higher order nonlinearities.

Breather-positon solutions are also compressed, but their period remains unaffected.

Abstract

In this paper, we investigate smooth positon and breather-positon solutions of a generalized nonlinear Schr\"{o}dinger (GNLS) equation which contains higher order nonlinear effects. With the help of generalized Darboux transformation (GDT) method we construct $N$th order smooth positon solutions of GNLS equation. We study the effect of higher order nonlinear terms on these solutions. Our investigations show that the positon solutions are highly compressed by higher order nonlinear effects. The direction of positons are also get changed. We also derive $N$th order breather-positon (B-P) solution with the help of GDT. We show that these B-Ps are well compressed by the effect of higher order nonlinear terms but the period of B-P solution is not affected as in the breather solution case.