With the aid of the truncated Painlev expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is ...With the aid of the truncated Painlev expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters.展开更多
For a one(2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special k...For a one(2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the B?cklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.展开更多
To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-P...To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-Petviashvili equation,which is a useful model in natural science,is established.By introducing an extended Backlund transformation and its bilinear formation,the symmetry breaking soliton,lump and breather solutions of this system are derived with the aid of some ansatze functions.Figures show these fascinating symmetry breaking structures of the explicit solutions.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11705077 and 11775104Natural Science Foundation of Zhejiang Province under Grant No.LY14A010005Scientific Research Foundation of the First-Class Discipline of Zhejiang Province(B)(No.201601)
文摘With the aid of the truncated Painlev expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters.
基金supported by the National Natural Science Foundation of China(Nos.11705077,11775104 and 11447017)。
文摘For a one(2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the B?cklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.
基金supported by the National Natural Science Foundation of China(Nos.11705077,11775104 and 11447017)the Natural Science Foundation of Zhejiang Province(No.LY14A010005)。
文摘To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-Petviashvili equation,which is a useful model in natural science,is established.By introducing an extended Backlund transformation and its bilinear formation,the symmetry breaking soliton,lump and breather solutions of this system are derived with the aid of some ansatze functions.Figures show these fascinating symmetry breaking structures of the explicit solutions.
