The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev6 method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems...The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev6 method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems. The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion （CTE） method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.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
基金Supported by the National Natural Science Foundation of China under Grant Nos.11305106,11405110,11305031,and 11275129the Natural Science Foundation of Zhejiang Province of China under Grant No.LQ13A050001the Natural Science Foundation of Guangdong Province under Grant No.S2013010011546
文摘The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev6 method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems. The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion （CTE） method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.
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.
