A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points xo, x1, xn depends on th orderings of ...A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points xo, x1, xn depends on th orderings of these points and it is locally independent of the permutation of first n - 1 points. Moreover we define reciprocal difference from another point of view, get the relation between inverse difference and reciprocal difference and obtain the property that the reciprocal difference is globally independent of the permutation of the points.展开更多
The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of ...The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.展开更多
In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule o...In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.展开更多
We derive the Lax pair and Darboux transformation for the(2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlev′e analysis. N-soliton solution in a compact determinant repr...We derive the Lax pair and Darboux transformation for the(2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlev′e analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively.展开更多
In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant re...In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant representation of Darboux transformation is used to derive soliton solutions,positon solutions to the IH-MB equations.展开更多
文摘A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points xo, x1, xn depends on th orderings of these points and it is locally independent of the permutation of first n - 1 points. Moreover we define reciprocal difference from another point of view, get the relation between inverse difference and reciprocal difference and obtain the property that the reciprocal difference is globally independent of the permutation of the points.
基金Project supported by the State Education Commission, the 973 Project "Nonlinear Science" the National Natural Science Foundation of China (No.9725104, No.19971084).
文摘The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
基金Supported by National Natural Science Foundation of China under Grant No.11331008China Postdoctoral Science Foundation Funded Sixtieth Batches(2016M602252)
文摘We derive the Lax pair and Darboux transformation for the(2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlev′e analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.11201251 and 11271210)Zhejiang Provincial Natural Science Foundation of China(Grant No.LY12A01007)+1 种基金the Natural Science Foundation of Ningbo(Grant No.2013A610105)K.C.Wong Magna Fund in Ningbo University
文摘In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant representation of Darboux transformation is used to derive soliton solutions,positon solutions to the IH-MB equations.
