The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the tw...The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.展开更多
Coupled Korteweg-de Vries(KdV)systems have many important physical applications.By considering a 4×4spectral problem,we derive a discrete coupled KdV-type equation hierarchy.Our hierarchy includes the coupled Vol...Coupled Korteweg-de Vries(KdV)systems have many important physical applications.By considering a 4×4spectral problem,we derive a discrete coupled KdV-type equation hierarchy.Our hierarchy includes the coupled Volterra system proposed by Lou et al.(e-print arXiv:0711.0420)as the first member which is a discrete version of the coupled KdV equation.We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11371248,11431008,11271254,11428102,and 11671255)the Fund from the Ministry of Economy and Competitiveness of Spain(Grant Nos.MTM2012-37070 and MTM2016-80276-P(AEI/FEDER,EU))
文摘The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.
基金Supported by the National Natural Science Foundation of China under Grant No 10971136also in part by the Ministry of Education and Science of Spain under Contract No MTM2009-12670.
文摘Coupled Korteweg-de Vries(KdV)systems have many important physical applications.By considering a 4×4spectral problem,we derive a discrete coupled KdV-type equation hierarchy.Our hierarchy includes the coupled Volterra system proposed by Lou et al.(e-print arXiv:0711.0420)as the first member which is a discrete version of the coupled KdV equation.We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.
