Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing ...Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.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
基金financially supported by the Scientific Research Foundation of North China University of Technology (Grant Nos.11005136024XN147-87 and 110051360024XN151-86)。
文摘Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.
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)
