In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian s...In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.展开更多
New type of variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained by using the source generation procedure.
The （2＋1）-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, re...The （2＋1）-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, respectively. It is shown that these solutions can be expressed as not only Pfaffians but also Wronskians and Grammians.展开更多
Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled ...Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.展开更多
Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a （3＋1）-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian exte...Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a （3＋1）-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.展开更多
1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact ...1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10771196 and 10831003the Natural Science Foundation of Zhejiang Province under Grant Nos.Y7080198 and R6090109
文摘In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.
基金Supported by the NSF of Henan Province(112300410109)Supported by the NSF of the Education Department(2010A110022)
文摘New type of variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained by using the source generation procedure.
基金supported by the National Natural Science Foundation of China(11202161 and 11172233)the Basic Research Fund of the Northwestern Polytechnical University(GBKY1034)
文摘The （2＋1）-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, respectively. It is shown that these solutions can be expressed as not only Pfaffians but also Wronskians and Grammians.
文摘Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932009 and 11172233)the Northwestern Polytechnical University Foundation for Fundamental Research, China (Grant No. GBKY1034)the State Administration of Foreign Experts Affairs of China, and the Chunhui Plan of the Ministry of Education of China
文摘Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a （3＋1）-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos. 10831003,61072147,11071159)+2 种基金the Shanghai Municipal Natural Science Foundation (No. 09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)TUBITAK (the Scientific and Technological Research Council of Turkey) for its financial support and grant for the research entitled "Integrable Systems and Soliton Theory" at University of South Florida
文摘1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.
