We explore the （2＋l）-dimensional dispersive long-wave （DLW） system. From the standard truncated Painleve expansion, the Baicklund transformation （BT） and residual symmetries of this system are derived. The intr...We explore the （2＋l）-dimensional dispersive long-wave （DLW） system. From the standard truncated Painleve expansion, the Baicklund transformation （BT） and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the （2＋l）-dimensional DLW system is consistent Riccati expansion （CRE） solvable. If the special form of （CRE）-consistent tanh-function expansion （CTE） is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem.展开更多
In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, ...In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.展开更多
Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Pain...Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.展开更多
For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the ...For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.展开更多
A predator prey interaction of both populations was treated by the Painlevé analysis method. The analytic solutions for the related equations was obtained using the truncated Painlevé expansion.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11371293 and 11505090)the Natural Science Foundation of Shaanxi Province,China(Grant No.2014JM2-1009)+1 种基金the Research Award Foundation for Outstanding Young Scientists of Shandong Province,China(Grant No.BS2015SF009)the Science and Technology Innovation Foundation of Xi’an,China(Grant No.CYX1531WL41)
文摘We explore the （2＋l）-dimensional dispersive long-wave （DLW） system. From the standard truncated Painleve expansion, the Baicklund transformation （BT） and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the （2＋l）-dimensional DLW system is consistent Riccati expansion （CRE） solvable. If the special form of （CRE）-consistent tanh-function expansion （CTE） is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11175092)the Scientific Research Fund of Education Department of Zhejiang Province of China (Grant No. Y201017148)K. C. Wong Magna Fund in Ningbo University
文摘In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.
基金Project supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the National Natural Science Foundation of China (Grant No. 10771072)
文摘Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.
基金Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ13A010014)the National Natural Science Foundation of China(Grant Nos.11326164,11401528,11435005,and 11375090)
文摘For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.
文摘A predator prey interaction of both populations was treated by the Painlevé analysis method. The analytic solutions for the related equations was obtained using the truncated Painlevé expansion.
