Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity

Monisha, S. Irudaya; Priya, N. Vishnu; Senthilvelan, M.; Rajasekar, S.

doi:10.1016/j.chaos.2022.112433

Cited by 11 publications

(1 citation statement)

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“…Following these advancements, endeavors have been made to construct smooth positon solutions for various nonlinear evolution equations, including the focusing mKdV equation [51], the complex mKdV equation [52], the derivative NLS equation [53,54], the NLS-Maxwell-Bloch equation [55], the higher-order Chen-Lee-Liu equation [56], and the Gerdjikov-Ivanov equation [57]. More recently, smooth positons and breather positons have been derived for the generalized NLS equation with higher-order nonlinearity along with higher-order solutions for an extended NLS equation featuring cubic and quartic nonlinearity [58,59]. Inspired by these advancements in the field of positons, our research aims to construct smooth positon solutions within the GP equation, incorporating time-varying nonlinearity and trap potentials.…”

Section: Introductionmentioning

confidence: 99%

Controlling Matter-Wave Smooth Positons in Bose–Einstein Condensates

Manikandan,

Serikbayev,

Vijayasree

et al. 2023

Symmetry

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In this investigation, we explore the existence and intriguing features of matter-wave smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter-wave smooth positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles. This study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or sech-like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we observe a rich variety of captivating behaviors in the matter-wave smooth positon profiles. These behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate density profile of matter-wave smooth positons in BECs, providing valuable insights into their controllable behavior and characteristics in the presence of time-modulated nonlinearity and trap potential effects.

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