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Residual Symmetry of the Alice-Bob Modified Korteweg-de Vries Equation
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作者 Ya-Hong Hu Zheng-Yi Ma Li Chen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2019年第5期489-495,共7页
Starting from the truncated Painlev′e expansion, the residual symmetry of the Alice-Bob modified Kortewegde Vries(AB-mKdV) equation is derived. The residual symmetry is localized and the AB-mKdV equation is transform... Starting from the truncated Painlev′e expansion, the residual symmetry of the Alice-Bob modified Kortewegde Vries(AB-mKdV) equation is derived. The residual symmetry is localized and the AB-mKdV equation is transformed into an enlarged system by introducing one new variable. Based on Lie's first theorem, the finite transformation is obtained from the localized residual symmetry. Further, considering the linear superposition of multiple residual symmetries gives rises to N-th B?cklund transformation in the form of the determinant. Moreover, the P_sT_d(the shifted parity and delayed time reversal) symmetric exact solutions(including invariant solution, breaking solution and breaking interaction solution) of AB-mKdV equation are presented and two classes of interaction solutions are depicted by using the particular functions with numerical simulation. 展开更多
关键词 Alice-Bob modified Korteweg-de Vries equation residual symmetry Backlund transformation PsTd symmetry explicit solution
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模糊c-均值算法在区域土壤预测制图中的应用 被引量:15
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作者 檀满枝 陈杰 《土壤学报》 CAS CSCD 北大核心 2009年第4期571-577,共7页
基于模糊c-均值算法和地统计学空间插值,在面积约为1km2的研究区内进行区域土壤预测制图。研究结果表明:根据研究区123个剖面和土钻样点,通过分析它们在形态学上的特征和定量属性,建立了9类诊断特征土层。通过FCM算法模型,获得4类最佳... 基于模糊c-均值算法和地统计学空间插值,在面积约为1km2的研究区内进行区域土壤预测制图。研究结果表明:根据研究区123个剖面和土钻样点,通过分析它们在形态学上的特征和定量属性,建立了9类诊断特征土层。通过FCM算法模型,获得4类最佳分类数,模糊指数为1.7。类别数目与研究区受地形、母质和土地利用方式影响的主要成土过程决定的土纲下土壤类型数目一致。将经过对称对数比转换的隶属度成分数据进行单一模糊类别隶属度土壤预测制图,4种类别土壤在空间上具有明显的渐变过渡特征,制图结果较理想。在单一类别隶属度土壤图的基础上生成最大隶属度土壤图,与常规土壤调查土壤图具有共同参比的基础。 展开更多
关键词 模糊逻辑 模糊C-均值算法 对称对数比转换 土壤空间预测制图
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Group-Invariant Solutions for the Generalised Fisher Type Equation
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作者 Kirsten Louw Raseelo J. Moitsheki 《Natural Science》 2015年第13期613-624,共12页
In this paper, we construct the group-invariant (exact) solutions for the generalised Fisher type equation using both classical Lie point and the nonclassical symmetry techniques. The generalised Fisher type equation ... In this paper, we construct the group-invariant (exact) solutions for the generalised Fisher type equation using both classical Lie point and the nonclassical symmetry techniques. The generalised Fisher type equation arises in theory of population dynamics. The diffusion term and coefficient of the source term are given as the power law functions of the spatial variable. We introduce the modified Hopf-Cole transformation to simplify a nonlinear second Order Ordinary Equation (ODE) into a solvable linear third order ODE. 展开更多
关键词 symmetry Methods modified Hopf-Cole transformation FISHER TYPE EQUATION EXACT Solutions
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Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches
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作者 Shoukry El-Ganaini Sachin Kumar Monika Niwas 《Journal of Ocean Engineering and Science》 SCIE 2023年第3期226-237,共12页
By taking advantage of three different computational analytical methods:the Lie symmetry analysis,the generalized Riccati equation mapping approach,and the modified Kudryashov approach,we construct multiple new analyt... By taking advantage of three different computational analytical methods:the Lie symmetry analysis,the generalized Riccati equation mapping approach,and the modified Kudryashov approach,we construct multiple new analytical soliton solutions to the nonlinear convection-diffusion-reaction equation(NCDR)with power-law nonlinearity and density-dependent diffusion.Lie symmetry analysis is one of the pow-erful techniques that reduce the higher-order partial differential equation into an ordinary differential equation by reduction of independent variables.By the Lie group technique,we obtain one-parameter in-variant transformations,determining equations and corresponding vectors for the considered convection-diffusion-reaction equation.By treating the parameters of the governing equation as constants,the ap-plied methods yield a variety of new closed-form solutions,including inverse function solutions,periodic solutions,exponential function solutions,dark solitons,singular solitons,combo bright-singular solitons,and the combine of bright-dark solitons and dark-bright solitons.Moreover,using the Bäcklund transfor-mation of the generalized Riccati equation and modified Kudryashov method,we can construct multiple solitons and other solutions of the considered equation.The obtained new solutions of this work demon-strate that the used approaches are powerful and effective in dealing with nonlinear equations,and that these solutions are required to explain many biological and physical phenomena.Comparing our obtained solutions of this paper with the ones obtained in the literature,we see that our solutions are new and not reported elsewhere.These newly formed soliton solutions will be more beneficial in the various dis-ciplines of ocean engineering,plasma physics,and nonlinear sciences. 展开更多
关键词 Lie symmetry analysis Generalized riccati equation mapping modified kudryashov approach Nonlinear convection-diffusion-reaction equation Solitary wave solutions Closed form solutions Backlund transformation Exact solution Dynamical wave structures Bäcklund transformation
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