The problem of soliton-soliton force is revisited. From the exact two solitons solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for arbitrary solitons amplitude difference, relative speed, phase, and separation. The latter allows for the investigation of soliton molecules formation, dynamics, and stability. We reveal the role of the time-dependent relative phase between the solitons in binding them in a soliton molecule. We derive its equilibrium bond length, spring constant, frequency, effective mass, and binding energy of the molecule. We investigate the molecule's stability against perturbations such as reflection from surfaces, scattering by barriers, and collisions with other solitons.
我们提出了一种由Dris { \it et al.}最近的实验所启发的形成物质波孤子分子的方法。在建议的设置中，我们表明，如果两个孤子最初准备在相位和足够小的分离和相对速度，一个绑定对将始终形成。这是验证直接数值模拟的Gross-Pitaevskii方程和两个孤子的精确相互作用能的推导，它采取的形式的Morse潜在的。这种相互作用势不仅取决于分离，而且还取决于孤子的相对相位，并且对于许多其他问题的分析处理是必不可少的，例如孤子气体和Toda孤子晶格。
Single impurity atom embedded in a dipolar two-soliton molecule as a qubit
King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；S. A. Azimov Physical-Technical Institute of Uzbekistan Academy of Sciences（乌兹别克斯坦科学院 S.A. 阿齐莫夫物理技术研究所）；Department of Physics, School of Science, The University of Jordan（约旦大学理学院物理系）；KFUPM（法赫德国王石油与矿产大学）
Dynamics of atomic and molecular solitary waves inatom-molecular hybrid Bose-Einstein condensates coupled by Magnetic Feshbach Resonance: Role of induced decays of Feshbach Molecules
