Periodic wave solutions and solitary wave solutions to a generalized （3＋1）-dimensional Gross Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homog...Periodic wave solutions and solitary wave solutions to a generalized （3＋1）-dimensional Gross Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to the similaritons reported in other nonlinear systems.展开更多
An improved homogeneous balance principle and an F-expansion technique are used to construct exactself-similar solutions to the cubic-quintic nonlinear Schrodinger equation.Such solutions exist under certain condition...An improved homogeneous balance principle and an F-expansion technique are used to construct exactself-similar solutions to the cubic-quintic nonlinear Schrodinger equation.Such solutions exist under certain conditions,and impose constraints on the functions describing dispersion,nonlinearity,and the external potential.Some simpleself-similar waves are presented.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 11172181)the Natural Science Foundation of Guangdong Province, China (Grant No. 10151200501000008)+1 种基金the Special Foundation of Talent Engineering of Guangdong Province, China (Grant No.2009109)the Scientific Research Foundation of Key Discipline of Shaoguan University, China(Grant No. ZD2009001)
文摘Periodic wave solutions and solitary wave solutions to a generalized （3＋1）-dimensional Gross Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to the similaritons reported in other nonlinear systems.
基金Supported by Natural Science Foundation of Zhejiang Province of China under Grant Nos.Y604106 and Y606182the Special Foundation of "University Talent Indraught Engineering" of Guangdong Province of China under Grant No.GDU2009109the Key Academic Discipline Foundation of Guangdong Shaoguan University under Gant No.KZ2009001
文摘An improved homogeneous balance principle and an F-expansion technique are used to construct exactself-similar solutions to the cubic-quintic nonlinear Schrodinger equation.Such solutions exist under certain conditions,and impose constraints on the functions describing dispersion,nonlinearity,and the external potential.Some simpleself-similar waves are presented.
