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
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
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
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 multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper...The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.展开更多
Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamic...Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.展开更多
In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1...In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model representing the wave propagation through incompressible fluids.The linearization of the wave structure in shallow water necessitates more critical wave capacity conditions than it does in deep water,and the strong nonlinear properties are perceptible.Some novel travelling wave solutions have been observed including solitons,kink,periodic and rational solutions with the aid of the latest computing tools such as Mathematica or Maple.The physical and analytical properties of several families of closed-form solutions or exact solutions and rational form function solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model problem are examined using Mathematica.展开更多
Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresp...Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.展开更多
In this paper, we consider (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Based on the bilinear form, we derive exact solutions of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation by using th...In this paper, we consider (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Based on the bilinear form, we derive exact solutions of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation by using the Wronskian technique, which include rational solutions, soliton solutions, positons and negatons.展开更多
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.
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.
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.
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the financial support from NBHM, India in the form of major research project, BRNS, India in the form of Young Scientist Research Award
文摘The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.
基金Supported by the National Natural Science Foundation of China(12275172)。
文摘Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.
文摘In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model representing the wave propagation through incompressible fluids.The linearization of the wave structure in shallow water necessitates more critical wave capacity conditions than it does in deep water,and the strong nonlinear properties are perceptible.Some novel travelling wave solutions have been observed including solitons,kink,periodic and rational solutions with the aid of the latest computing tools such as Mathematica or Maple.The physical and analytical properties of several families of closed-form solutions or exact solutions and rational form function solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model problem are examined using Mathematica.
基金supported by the National Natural Science Foundation of China (Grant Nos.12275085 and 12235007)the Science and Technology Commission of Shanghai Municipality (Grant No.22DZ2229014)。
文摘Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.
文摘In this paper, we consider (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Based on the bilinear form, we derive exact solutions of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation by using the Wronskian technique, which include rational solutions, soliton solutions, positons and negatons.
