A complete scalar classification for dark Sharma-Tasso-Olver＇s（STO＇s） equations is derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every cl...A complete scalar classification for dark Sharma-Tasso-Olver＇s（STO＇s） equations is derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark STO systems, thus some special equations including symmetry equation and dual symmetry equation are obtained by selecting a free parameter. Furthermore, the recursion operators of STO equation and dark STO systems are constructed by a direct assumption method.展开更多
When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The q...When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.展开更多
In this letter,we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal sym...In this letter,we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system.展开更多
Nel corso del 1991 è stato effettuato un censimento delle tane di Tasso Meles melesin un’area molto antropizzata della Pianura Padana posta alla conflaenza del flume Lambro nel flumePo, estesa per 103 Km^2. Si s...Nel corso del 1991 è stato effettuato un censimento delle tane di Tasso Meles melesin un’area molto antropizzata della Pianura Padana posta alla conflaenza del flume Lambro nel flumePo, estesa per 103 Km^2. Si sono individuate 24 tane (0,2 Km^2). Density and distribution of Badger’s setts (Meles meles) in the Lower Lodigiano (NorthernItaly). A census of the Badger’s setts (Meles meles) was carried out in 1991 in a densely inhabited areaof the Po Plain, near the mouth of the river Lambro into the Po. In the study area (extended for103 Km^2) 24 setts have been found (0,2 Km^2).展开更多
A hierarchy of new nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is derived.One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation.Then infinit...A hierarchy of new nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is derived.One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation.Then infinitely many conservation laws of this equation are deduced.Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.展开更多
Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivat...Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11775121,11775116 and 11435005the Ningbo Natural Science Foundation of China under Grant No 2015A610159the K.C.Wong Magna Fund in Ningbo University
文摘A complete scalar classification for dark Sharma-Tasso-Olver＇s（STO＇s） equations is derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark STO systems, thus some special equations including symmetry equation and dual symmetry equation are obtained by selecting a free parameter. Furthermore, the recursion operators of STO equation and dark STO systems are constructed by a direct assumption method.
文摘When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.
基金Supported by National Natural Science Foundation of China under Grant Nos.1120509211175092 and 11435005+2 种基金Ningbo Natural Science Foundation under Grant Nos.2015A610159 and 2012A610178by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzw11502the authors were sponsored by K.C.Wong Magna Fund in Ningbo University
文摘In this letter,we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system.
文摘Nel corso del 1991 è stato effettuato un censimento delle tane di Tasso Meles melesin un’area molto antropizzata della Pianura Padana posta alla conflaenza del flume Lambro nel flumePo, estesa per 103 Km^2. Si sono individuate 24 tane (0,2 Km^2). Density and distribution of Badger’s setts (Meles meles) in the Lower Lodigiano (NorthernItaly). A census of the Badger’s setts (Meles meles) was carried out in 1991 in a densely inhabited areaof the Po Plain, near the mouth of the river Lambro into the Po. In the study area (extended for103 Km^2) 24 setts have been found (0,2 Km^2).
基金Supported by National Natural Science Foundation of China under Grant Nos.11171312 and 11126308Science and Technology Research Key Projects of the Education Department of Henan Province under Grant No.12A110023
文摘A hierarchy of new nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is derived.One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation.Then infinitely many conservation laws of this equation are deduced.Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.
文摘Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.
基金Research supported by the National Natural Science Foundation of China(10671168)the Natural Science Foundation of Jiangsu Province(BK2006032)+1 种基金the Foundation of‘Liu Da Ren Cai’Plan(06-A-038)the Foundation of‘333 Gongcheng’of Jiangsu Province
