Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation al...Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.展开更多
Effect of different noise reduction measures for diesel engines was evaluated based on hierarchy diagnosis. The hierarchy diagnosis chart and hierarchy judgment matrix were given. Through evaluation of noise reduction...Effect of different noise reduction measures for diesel engines was evaluated based on hierarchy diagnosis. The hierarchy diagnosis chart and hierarchy judgment matrix were given. Through evaluation of noise reduction measures, the main strategies of noise reduction were found. The result shows that the noise reduction level of different frequency belts varies from measure to measure. The reduction capacity of different measures could not add simply, which relates to the problem of parameter matching.展开更多
This paper analyzes the reduction of the well known Kadomtsev-Petviashvili hierarchy. The reduction yields a previously unknown dispersion counterpart of the dispersionless hierarchy which has a Lax function of the fo...This paper analyzes the reduction of the well known Kadomtsev-Petviashvili hierarchy. The reduction yields a previously unknown dispersion counterpart of the dispersionless hierarchy which has a Lax function of the form p＋u（x）（p-φ）^-1＋v（x）（p-φ）^-2. This paper also describes the bihamiltonian structure of the reduced hierarchy using Dirac reduction and proves that the approximation for the reduced hierarchy up to the second order of the dispersion parameter coincides with the hierarchy of integrable systems constructed from a particular twodimensional Frobenius manifold using the approach of Dubrovin and Zhang.展开更多
In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarch...In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the periodic ex2DTLH, sinh-Gordon equation with self-consistent sources and one-dimensional Toda lattice hierarchy with self-consistent sources. The general solutions of reduced hierarchies are found from the Casoratian solutions of ex2DTLH, by considering additional constraints during the dressing procedure.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12235007, 11975131, and 12275144)the K. C. Wong Magna Fund in Ningbo Universitythe Natural Science Foundation of Zhejiang Province of China (Grant No. LQ20A010009)
文摘Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.
基金Supported by China Postdoctoral Science Foundation (No.20060400193)Yunnan Foundation for Science and Technology Cooperation between Government and University(No.2003HBBAA02A049) .
文摘Effect of different noise reduction measures for diesel engines was evaluated based on hierarchy diagnosis. The hierarchy diagnosis chart and hierarchy judgment matrix were given. Through evaluation of noise reduction measures, the main strategies of noise reduction were found. The result shows that the noise reduction level of different frequency belts varies from measure to measure. The reduction capacity of different measures could not add simply, which relates to the problem of parameter matching.
文摘This paper analyzes the reduction of the well known Kadomtsev-Petviashvili hierarchy. The reduction yields a previously unknown dispersion counterpart of the dispersionless hierarchy which has a Lax function of the form p＋u（x）（p-φ）^-1＋v（x）（p-φ）^-2. This paper also describes the bihamiltonian structure of the reduced hierarchy using Dirac reduction and proves that the approximation for the reduced hierarchy up to the second order of the dispersion parameter coincides with the hierarchy of integrable systems constructed from a particular twodimensional Frobenius manifold using the approach of Dubrovin and Zhang.
基金supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028the Natural Science Foundation of Fujian Province under Grant No.2008J0199
文摘我们第一分别地基于特徵函数对称减小和非标准的减小建议二种新多部件 BKP (mcBKP ) 层次。第一种与其宽松的代表被介绍的前後一致的来源一起包含 BKP 方程的二种类型。两个承认的二个 mcBKP 层次减小到抑制 k 的 BKP 层次并且到与前後一致的来源一起的维的层次，它包括二与前後一致的来源一起与前後一致的来源一起并且双向 SK 方程 SK 方程打的 integrable (1+1 ) 。
基金supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)National Natural Science Foundation of China (Grant Nos. 10801083, 10901090)+1 种基金Chinese Universities Scientific Fund (Grant No. 2009-2-05)the Basic Research Fund of China Agricultural University (Grant No. 2007036)
文摘In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the periodic ex2DTLH, sinh-Gordon equation with self-consistent sources and one-dimensional Toda lattice hierarchy with self-consistent sources. The general solutions of reduced hierarchies are found from the Casoratian solutions of ex2DTLH, by considering additional constraints during the dressing procedure.
