In this paper, we present an object reduction for nonlinear partial differential equations. As a concrete example of its applications in physical problems, this method is applied to the （2＋1）-dimensional Boiti-Leon...In this paper, we present an object reduction for nonlinear partial differential equations. As a concrete example of its applications in physical problems, this method is applied to the （2＋1）-dimensional Boiti-Leon-Pempinelli system, which has the extensive physics background, and an abundance of exact solutions is derived from some reduction equations. Based on the derived solutions, the localized structures under the periodic wave background are obtained.展开更多
With the help of the symbolic computation system Maple, the Riccati equation mapping approach and a linear variable separation approach, a new family of complex solutions for the （2＋ 1）-dimensional Boiti-Leon-Pempi...With the help of the symbolic computation system Maple, the Riccati equation mapping approach and a linear variable separation approach, a new family of complex solutions for the （2＋ 1）-dimensional Boiti-Leon-Pempinelli system （BLP） is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations are obtained.展开更多
A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon Pe...A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.展开更多
The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supe...The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely f（t）. Some interesting special cases of symmetry algebras are commutativity of higher order generalized symmetries. many generalized symmetries with an arbitrary function presented, including a limit case f（t） = 1 related to the展开更多
In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated ...In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.展开更多
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106 and the Natural Science Foundation of Zhejiang Lishui University under Grant No. FC06001
文摘In this paper, we present an object reduction for nonlinear partial differential equations. As a concrete example of its applications in physical problems, this method is applied to the （2＋1）-dimensional Boiti-Leon-Pempinelli system, which has the extensive physics background, and an abundance of exact solutions is derived from some reduction equations. Based on the derived solutions, the localized structures under the periodic wave background are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant No.11375079)the Natural Science Foundation of Zhejiang Province,China(Grant Nos.Y6100257 and Y6110140)
文摘With the help of the symbolic computation system Maple, the Riccati equation mapping approach and a linear variable separation approach, a new family of complex solutions for the （2＋ 1）-dimensional Boiti-Leon-Pempinelli system （BLP） is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations are obtained.
文摘A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.
基金supported by the National Natural Science Foundation of China(Grant Nos.11275123,11175092,11475052,and 11435005)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)the Talent Fund and K C Wong Magna Fund in Ningbo University,China
文摘The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely f（t）. Some interesting special cases of symmetry algebras are commutativity of higher order generalized symmetries. many generalized symmetries with an arbitrary function presented, including a limit case f（t） = 1 related to the
文摘In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.
