This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨...This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨ cklund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons.展开更多
In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applicati...In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten-Krasil'shchik coupled KdV-mKdV system.展开更多
In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science etc.We build Bäcklund transformations and residual symme...In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science etc.We build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevétruncated expansion approach.We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group.In this transformation group,we deliver new exact solution profiles via the combination of various simple(seed and tangent hyperbolic form)exact solution structures.In this manner,we acquire an infinite amount of exact solution forms methodically.Furthermore,we demonstrate that the model may be integrated in terms of consistent Riccati expansion.Using the Maple symbolic program,we derive the exact solution forms of solitary-wave and soliton-cnoidal interaction.Through 3D and 2D illustrations,we observe the dynamic analysis of the acquired solution forms.展开更多
文摘This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨ cklund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons.
基金supported by the National Natural Science Foundation of China (Grant Nos.12175111,11931107 and 12171474)NSFC-RFBR (Grant No.12111530003)。
文摘In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten-Krasil'shchik coupled KdV-mKdV system.
基金Supported by National Science Foundation of China ( Grant No. 60973146)National Science Foundation of Shandong Province,China(Grant No. 2R2009GM036)Foundation for Study Encouragement to Middel-aged and Young Scientists of Shandong Province,China(Grant No.2008BS01019)
基金Supported by the National Natural Science Foundation of China under Grant 61072145the Scientific Research Project of Beijing Educational Committee(SQKM201211232016)Beijing Excellent Talent Training Project(2013D005007000003)
文摘In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science etc.We build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevétruncated expansion approach.We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group.In this transformation group,we deliver new exact solution profiles via the combination of various simple(seed and tangent hyperbolic form)exact solution structures.In this manner,we acquire an infinite amount of exact solution forms methodically.Furthermore,we demonstrate that the model may be integrated in terms of consistent Riccati expansion.Using the Maple symbolic program,we derive the exact solution forms of solitary-wave and soliton-cnoidal interaction.Through 3D and 2D illustrations,we observe the dynamic analysis of the acquired solution forms.
