Dark soliton solution of the three-dimensional Gross-Pitaevskii equation with an isotropic harmonic potential and nonlinearity in polytropic approximation

2016 ◽  
Vol 68 (3) ◽  
pp. 383-386
Author(s):  
Xinwei Fan ◽  
Yu Zhou ◽  
Yalun Li ◽  
Ying Wang ◽  
Shuyu Zhou
Keyword(s):  
Soliton Solution ◽  
Three Dimensional ◽  
Dark Soliton ◽  
Harmonic Potential ◽  
Pitaevskii Equation

Dark soliton solution of Sasa-Satsuma equation

2010 ◽  
Author(s):  
Y. Ohta ◽  
Wen Xiu Ma ◽  
Xing-biao Hu ◽  
Qingping Liu
Keyword(s):  
Soliton Solution ◽  
Dark Soliton

scholarly journals Soliton Model of the Photon / Fotona Solitona Modelis

2013 ◽  
Vol 50 (2) ◽  
pp. 60-67 ◽  
Author(s):  
I. Bersons
Keyword(s):  
Nonlinear Equation ◽  
Soliton Solution ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
Soliton Model ◽  
Dimensionless Constant ◽  
Dimensional Object ◽  
Dimensional Soliton ◽  
Wave Properties

A three-dimensional soliton model of photon with corpuscular and wave properties is proposed. We consider the Maxwell equations and assume that light induces the polarization and magnetization of vacuum only along the direction of its propagation. The nonlinear equation constructed for the vector potential is similar to the generalized nonlinear Schrödinger equation and comprises a dimensionless constant μ that determines the size-scale of soliton and is expected to be small. The obtained one-soliton solution of the proposed nonlinear equation describes a three-dimensional object identified as photon.

Localized waves and interaction solutions to an extended (3+1)-dimensional Kadomtsev–Petviashvili equation

2020 ◽  
Vol 34 (06) ◽  
pp. 2050076 ◽  
Author(s):  
Han-Dong Guo ◽  
Tie-Cheng Xia ◽  
Wen-Xiu Ma
Keyword(s):  
Three Dimensional ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Complex Conjugate ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Parameter Constraints ◽  
Localized Waves

In this paper, an extended (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied via the Hirota bilinear derivative method. Soliton, breather, lump and rogue waves, which are four types of localized waves, are obtained. N-soliton solution is derived by employing bilinear method. Then, line or general breathers, two-order line or general breathers, interaction solutions between soliton and line or general breathers are constructed by complex conjugate approach. These breathers own different dynamic behaviors in different planes. Taking the long wave limit method on the multi-soliton solutions under special parameter constraints, lumps, two- and three-lump and interaction solutions between dark soliton and dark lump are constructed, respectively. Finally, dark rogue waves, dark two-order rogue waves and related interaction solutions between dark soliton and dark rogue waves or dark lump are also demonstrated. Moreover, dynamical characteristics of these localized waves and interaction solutions are further vividly demonstrated through lots of three-dimensional graphs.

scholarly journals Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT

2016 ◽  
Vol 19 (5) ◽  
pp. 1141-1166 ◽  
Author(s):  
Weizhu Bao ◽  
Qinglin Tang ◽  
Yong Zhang
Keyword(s):  
Numerical Methods ◽  
Ground State ◽  
High Efficiency ◽  
Three Dimensional ◽  
Ground States ◽  
Dipole Interaction ◽  
Polar Coordinates ◽  
Pitaevskii Equation ◽  
Nonuniform Fft ◽  
Bose Einstein

AbstractWe propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented with the non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the corresponding two-dimensional (2D) model under a strongly anisotropic confining potential. Different from existing methods, the NUFFT based DDI solver removes the singularity by adopting the spherical/polar coordinates in the Fourier space in 3D/2D, respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary and/or needed. Then, we incorporate this solver into existing successful methods for computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our new methods outperform existing methods in terms of both accuracy and efficiency.

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