With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation ...With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the(3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.展开更多
The nonlocal symmetry of the Sawada–Kotera(SK)equation is constructed with the known Lax pair.By introducing suitable and simple auxiliary variables,the nonlocal symmetry is localized and the finite transformation an...The nonlocal symmetry of the Sawada–Kotera(SK)equation is constructed with the known Lax pair.By introducing suitable and simple auxiliary variables,the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further.On the other hand,the group invariant solutions of the SK equation are constructed with the classic Lie group method.In particular,by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.展开更多
In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)...In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1),(2+1) and(3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11835011 and 12074343)。
文摘With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the(3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.
基金supported by the National Natural Science Foundation of China,Grant No.11835011 and Grant No.11675146。
文摘The nonlocal symmetry of the Sawada–Kotera(SK)equation is constructed with the known Lax pair.By introducing suitable and simple auxiliary variables,the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further.On the other hand,the group invariant solutions of the SK equation are constructed with the classic Lie group method.In particular,by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.
基金Supported by the National Natural Science Foundation of China under Grant No.61671227the Natural Science Foundation of Shandong Province in China under Grant No.ZR2014AM018
文摘In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1),(2+1) and(3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.
