Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation

The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations. In this paper, we use a new form of variable separation to study novel soliton molecules and their interactions in (2+1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation. Dromion molecules, ring molecules, lump molecules, multi-instantaneous molecules, and their interactions are obtained. Then we draw corresponding images with maple software to study their dynamic behavior.     

任意方程法及BKP方程新的精确解

In this paper,auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation.We study the(2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions.The method used here can be also extended to other nonlinear partial differential equations.     

New Periodic Solution to Jacobi Elliptic Functions of a （2d-1）-Dimensional BKP Equation and a Generalized Klein-Gordon Equation

With the help of the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to obtain the Jacobi doubly periodic wave solutions of the （2＋1）-dimensional B-type Kadomtsev-Petviashvili （BKP） equation and the generalized Klein-Gordon equation. The method is also valid for other （1＋1）-dimensional and higher dimensional systems.     

Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance

We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetric soliton by changing the parameterφ.In addition,the collision between soliton molecules(or asymmetric soliton)and several soliton solutions is observed.Finally,some related pictures are presented.     

近环的理想与导子

设Ｎ是中心为Ｚ的素近环,Ｉ是Ｎ的右理想,Ｄ是Ｎ上的非平凡导子,本文证明了１）若Ｄ（Ｉ）∈Ｚ,则（Ｎ１＋）是交换的;又若Ｎ２－挠自由,则Ｎ是无零因子交换环,（２）若０≠Ｄ＾ｎ（Ｉ）∈Ｚ,Ｄ＾ｎ－１（Ｉ）∈Ｉ,且Ｎ是（ｎ＋１）１挠自由的,则Ｎ是无零因子交换环。