Hirota method for the nonlinear Schr\H{o}dinger equation with an arbitrary linear time-dependent potential

TL;DR

This paper develops a Hirota method to analytically construct soliton solutions for the nonlinear Schrödinger equation with arbitrary time-dependent linear potentials, relevant to Bose-Einstein condensates.

Contribution

It introduces a novel Hirota-based approach for solving the nonlinear Schrödinger equation with arbitrary time-dependent linear potentials, enabling explicit soliton solutions.

Findings

Analytical one- and two-soliton solutions derived

Method applicable to Bose-Einstein condensate dynamics

Enhanced understanding of soliton behavior under time-dependent potentials

Abstract

In this paper, a Hirota method is developed for applying to the nonlinear Schr\"odinger equation with arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensation. The nonlinear Schr\"odinger equation is decoupled to two equations carefully. With a reasonable assumption the one- and two-soliton solutions are constructed analytically in the presence of an arbitrary time-dependent linear potential.