We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitae...We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.展开更多
Based on the Wronskian technique and Lax pair,double Wronskian solution of the nonisospectral BKP equation is presented explicitly.The speed and dynamical influence of the one soliton are discussed.Soliton resonances ...Based on the Wronskian technique and Lax pair,double Wronskian solution of the nonisospectral BKP equation is presented explicitly.The speed and dynamical influence of the one soliton are discussed.Soliton resonances of two soliton are shown by means of density distributions.Soliton properties are also investigated in the inhomogeneous media.展开更多
In this work,the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus,which is a semi-discrete version of Harrison and Estabrook’s geometric approach.A four-...In this work,the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus,which is a semi-discrete version of Harrison and Estabrook’s geometric approach.A four-dimensional Lie algebra and its one-,two-and three-dimensional subalgebras are given.Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors.展开更多
基金Acknowledgements We would like to express our sincere thanks to Z. X. Liangang L. Wu for their original works and figures. This work was supported by the NatiorLM Natural Science Foundation of China （Grant Nos. 10874235, 10934010, and 60978019）, the National Key Basic Research Special Foundation of China （Grant Nos. 2009CB930701, 2010CB922904, and 2011CB921500）.
文摘We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.
基金Supported by the Research Committee of The Hong Kong Polytechnic University under Grant No.G-YM37the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics under Grant No.1-ZVA8+3 种基金National Natural Science Foundation of China under Grant Nos.11271362 and 11375030Beijing Natural Science Fund Project and Beijing City Board of Education Science and Technology Key Project under Grant No.KZ201511232034Beijing Natural Science Foundation under Grant No.1153004,Beijing Nova Program No.Z131109000413029Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No.2014000026833ZK19
文摘Based on the Wronskian technique and Lax pair,double Wronskian solution of the nonisospectral BKP equation is presented explicitly.The speed and dynamical influence of the one soliton are discussed.Soliton resonances of two soliton are shown by means of density distributions.Soliton properties are also investigated in the inhomogeneous media.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375030,11472315Department of Science and Technology of Henan Province under Grant No.162300410223Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No.2014000026833ZK19
文摘In this work,the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus,which is a semi-discrete version of Harrison and Estabrook’s geometric approach.A four-dimensional Lie algebra and its one-,two-and three-dimensional subalgebras are given.Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors.
