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| 1 | Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation显示文摘A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions.The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries,leading to the conservation laws and the reduction of the wave equations.Some exact solutions of the considered wave equations for particular cases are derived. | Yinshan YUN Chaolu TEMUER | 2015 | Applied Mathematics and Mechanics(English Edition)2015，36，3： | 4 |
| 2 | Symmetry analysis of modified 2D Burgers vortex equation for unsteady case显示文摘In this paper, a symmetry analysis of the modified 2D Burgers vortex equation with a flow parameter is presented. A general form of classical and non-classical symmetries of the equation is derived. These are fundamental tools for obtaining exact solutions to the equation. In several physical cases of the parameter, the specific classical and non-classical symmetries of the equation are then obtained. In addition to rediscovering the existing solutions given by different methods, some new exact solutions are obtained with the symmetry method, showing that the symmetry method is powerful and more general for solving partial differential equations(PDEs). | Lihua LIU Chaolu TEMUER | 2017 | Applied Mathematics and Mechanics(English Edition)2017，38，3： | 2 |
| 3 | An algorithm for the complete symmetry classification of differential equations based on Wu's method显示文摘 | Temuer C | 2010 | J Eng Math2010，66，： | 1 |
| 4 | ANALYTIC SOLUTION AND NUMERICAL SOLUTION TO ENDOLYMPH EQUATION USING FRACTIONAL DERIVATIVE显示文摘In this paper,we study the solution to the endolymph equation using the fractional derivative of arbitrary orderλ(0<λ<1).The exact analytic solution is given by using Laplace transform in terms of Mittag-Leffler functions.We then evaluate the approximate numerical solution using MATLAB. | Duan Junsheng Liu Zhenhang Zhang Fengkuan Temuer Chaolu | 2008 | Annals of Differential Equations2008，24，1： | 1 |
| 5 | Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method显示文摘This paper extends a method, called bilinear neural network method(BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model,specific activation functions of '2-2' model and arbitrary functions of '2-2-3' model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gB KP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots,the evolution characteristic of these waves are exhibited. | ZHANG Runfa BILIGE Sudao CHAOLU Temuer | 2021 | Journal of Systems Science & Complexity2021，34，1： | 1 |
| 6 | An algorithm for the complete symmetry classification of differential equations based on Wu's method显示文摘 | Temuer C L Pang J | 2010 | Journal of Engineering Mathematics2010，66，13： | 1 |
| 7 | Nonclassical Symmetry of the Wave Equation with Source Term显示文摘 | Temuer C L Eerdun B H Xia T C | 2012 | Chinese Annals of Mathematics (Series A )2012，33，2： | 1 |
| 8 | Local and nonlocal symmetries for nonlinear telegraph equations显示文摘 | Bluman G W Temuer C L | 2005 | J Math Phys2005，46，02： | 1 |
| 9 | Comparing symmetries and conservation law s of nonlinear telegarph equation显示文摘 | Bluman G W Temuer C L | 2005 | J Math Phys2005，46，07： | 1 |
| 10 | An extended simplest equation method and its application to several forms of the fifth-order KdV equation显示文摘 | Sudao Bilige Temuer Chaolu | 2010 | Applied Mathematics and Computation2010，216，： | 1 |
| 11 | Two Generalizations of the(G/G)- Expansion Method and Their Applications 显示文摘 | Sudao Bilige Temuer Chaolu | 2010 | Journal of Inner Mongolia University :Natural Science Edition2010，41，2： | 1 |
| 12 | An extended simplest equation method and its application to several forms of the fifth-order KdV equation显示文摘 | Sudao Bilige Temuer Chaolu | 2010 | Appl Math Comput2010，216，： | 1 |
| 13 | Application of the extended simplest equation method to the coupled Schrdinger-Boussinesq equation显示文摘 | Sudao Bilige Temuer Chaolu Wang X M | 2013 | Appl Math Comput2013，224，： | 1 |
| 14 | An extended simplest equationmethod and its application to several forms of the fifth-order KdV equa-tion显示文摘 | BILIGE SUDAO CHAOLU TEMUER | 2010 | Appl Math Comput2010，216，： | 1 |
| 15 | SCALE-INVARIANT SOLUTION FOR FRACTIONAL ANOMALOUS DIFFUSION EOUATION显示文摘Fractional diffusion equation for transport phenomena in fractal media is an integro-partial differential equation. For solving the problem of this kind of equation the invariants of the group of scaling transformations are given and then used for deriving the integro-ordinary differential equation for the scale-invariant solution. With the help of Mellin transform the scale-invariant solution is obtained in terms of Fox functions. And the series and asymptotic representations for the solution are considered. | Duan Junsheng Temuer Chaolu | 2006 | Annals of Differential Equations2006，22，1： | 1 |
| 16 | An extended simplest equation method and its application to several forms of the fifth-order KdV equation显示文摘 | Sudao Bilige Temuer Chaolu | 2010 | Appl Math Comput2010，216，11： | 1 |
| 17 | Application of the extended simplest equation method to the coupled Schr?dinger–Boussinesq equation显示文摘 | Sudao Bilige Temuer Chaolu Xiaomin Wang | 2013 | Applied Mathematics and Computation2013，，： | 1 |
| 18 | A Generalized G'/G-Expansion Method and Its Application显示文摘 | Sudao Bilige Temuer Chaolu | | 0，，01： | 1 |
| 19 | Two generalizations of the (G'/G)-expansion method and their applicatiom显示文摘 | Sudao Bilige Temuer Chaolu | 2010 | Journal of Inner Mongolia University2010，41，2： | 1 |
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