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New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov EquationsUsing General Projective Riccati Equation Method 被引量:14
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作者 CHENYong LIBiao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第1期1-6,共6页
Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer alg... Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions. 展开更多
关键词 projective riccati equation method generalized Zakharov-Kuzentsov equation exact solutions
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Double-Parameter Solutions of Projective Riccati Equations and Their Applications 被引量:1
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作者 WANG Ming-Liang LI Er-Qiang LI Xiang-Zheng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第1期1-9,共9页
The purpose of the present paper is twofold. First, the projective Riccati equations (PREs for short) are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values o... The purpose of the present paper is twofold. First, the projective Riccati equations (PREs for short) are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^+ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered. 展开更多
关键词 projective riccati equations linearized theorem homogeneous balance Sub-ODE method travelling wave solutions nonlinear PDE
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Application of Extended Projective Riccati Equation Method to(2+1)-Dimensional Broer-Kaup-Kupershmidt System 被引量:1
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作者 LU Bin ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期814-820,共7页
In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pro... In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations. 展开更多
关键词 nonlinear- partial differential equations extended projective riccati equation method exact solutions Broer- Kaup Kupershmidt system
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Extended Generalized Riccati Equation Mapping for Thermal Traveling-Wave Distribution in Biological Tissues through a Bio-Heat Transfer Model with Linear/Quadratic Temperature-Dependent Blood Perfusion 被引量:1
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作者 Emmanuel Kengne Fathi Ben Hamouda Ahmed Lakhssassi 《Applied Mathematics》 2013年第10期1471-1484,共14页
Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended g... Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues. 展开更多
关键词 Bio-Heat Transfer Pennes Bio-Heat Model TEMPERATURE-DEPENDENT Blood Perfusion thermal therapy EXTENDED generalized riccati equation MAPPING method
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A New Generalized Riccati Equation Rational Expansion Method to Generalized Burgers-Fisher Equation with Nonlinear Terms of Any Order 被引量:1
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作者 ZHANG Xiao-Ling WANG Jing ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期779-786,共8页
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution eq... In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order. 展开更多
关键词 generalized riccati equation rational expansion method generalized Burgers-Fisher equation with nonlinear terms of any order symbolic computation
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Novel loop-like solitons for the generalized Vakhnenko equation
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作者 张旻 马玉兰 李帮庆 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第3期271-274,共4页
A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary f... A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary function of an independent variable.Based on the solution,two hyperbolic functions are chosen to construct new solitons.Novel single-loop-like and double-loop-like solitons are found for the equation. 展开更多
关键词 generalized Vakhnenko equation extended riccati mapping method nontraveling wave solution loop-like soliton
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New Multiple Soliton-like and Periodic Solutions for (2+l)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 被引量:3
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作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期793-798,共6页
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit ... In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients. 展开更多
关键词 (2+1)-dimensional canonical generalized (CGKP) equation with variable coefficients tanh function method riccati equation soliton-like and periodic solutions
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Exact Solutions of Generalized Burgers-Fisher Equation with Variable Coefficients 被引量:1
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作者 陈博奎 闵松强 汪秉宏 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期443-449,共7页
The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and som... The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and some of which are derived for the first time. It is concluded from the results that this approach is simple and efficient even in solving partial differential equations with variable coefficients. 展开更多
关键词 generalized riccati equation rational expansion method generalized variable coefficient Burgers-Fisher equation exact solution
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New Complexiton Solutions for the(2+1)-dimensional Burgers Equation
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作者 李文婷 陈续升 张鸿庆 《Northeastern Mathematical Journal》 CSCD 2007年第5期453-463,共11页
In this paper, a new generalized compound Riccati equations rational expansion method (GCRERE) is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method... In this paper, a new generalized compound Riccati equations rational expansion method (GCRERE) is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method is not only recover some known solutions, but also find some new and general complexiton solutions. Being concise and straightforward, it is applied to the (2+1)-dimensional Burgers equation. As a result, eight families of new exact analytical solutions for this equation are found. The method can also be applied to other nonlinear partial differential equations. 展开更多
关键词 generalized compound riccati equations rational expansion method (2+1)-dimensional Burgers equation complexiton solution
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广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解 被引量:22
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作者 智红燕 陈勇 张鸿庆 《数学物理学报(A辑)》 CSCD 北大核心 2005年第S1期956-964,共9页
助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方 法,即改进的广义射影Ricccati方程方法,求解(2+1)维色散长波方程,得到该方程的新的 更一般形式的行波解,包括扭状孤波解,钟状解,孤子解和周期解.并对部... 助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方 法,即改进的广义射影Ricccati方程方法,求解(2+1)维色散长波方程,得到该方程的新的 更一般形式的行波解,包括扭状孤波解,钟状解,孤子解和周期解.并对部分新形式孤波解画 图示意. 展开更多
关键词 广义射影riccati方程方法 (2+1)维色散长波方程 行波解
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一类Riccati矩阵方程广义自反解的双迭代算法 被引量:3
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作者 张凯院 王娇 《数学杂志》 CSCD 北大核心 2015年第2期469-476,共8页
本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广... 本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广义自反解的双迭代算法.拓宽了求解非线性矩阵方程的迭代算法.数值算例表明双迭代算法是有效的. 展开更多
关键词 riccati矩阵方程 广义自反解 牛顿算法 修正共轭梯度法 双迭代算法
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应用Riccati-Bernoulli辅助方程求解广义非线性Schrodinger方程和(2+1)维非线性Ginzburg-Landau方程 被引量:7
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作者 石兰芳 王明灿 钱正雅 《应用数学和力学》 CSCD 北大核心 2020年第7期786-795,共10页
研究了Riccati-Bernoulli辅助方程法,并应用这种方法得到广义非线性Schrodinger方程和(2+1)维非线性Ginzburg-Landau方程的精确行波解.这些解包括有理函数、三角函数、双曲函数和指数函数.应用这种方法求解过程简洁有效.该研究对于数学... 研究了Riccati-Bernoulli辅助方程法,并应用这种方法得到广义非线性Schrodinger方程和(2+1)维非线性Ginzburg-Landau方程的精确行波解.这些解包括有理函数、三角函数、双曲函数和指数函数.应用这种方法求解过程简洁有效.该研究对于数学物理方程领域诸多非线性偏微分方程精确解的探究具有重要的意义. 展开更多
关键词 riccati-Bernoulli辅助方程法 广义非线性Schrodinger方程 (2+1)维非线性Ginzburg-Landau方程 行波解
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利用微分算子法研究二阶齐次线性微分方程与Riccati方程通解之联系 被引量:4
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作者 林庆泽 《海南师范大学学报(自然科学版)》 CAS 2017年第3期237-242,共6页
文章应用微分算子法处理二阶变系数线性微分方程,揭示了二阶齐次变系数线性微分方程与Riccati方程的通解理论之间的联系,发现这两类方程之间的通解可以互相转化,同时给出转化的途径.最后,作为理论的应用分析了一些具体例子.
关键词 算子法 微分方程 riccati方程 通解
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New solutions for four novel generalized nonlinear fractional fifth-order equations
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作者 Mehmet Senol Lanre Akinyemi +1 位作者 Henrietta Nkansah Waleed Adel 《Journal of Ocean Engineering and Science》 SCIE 2024年第1期59-65,共7页
In this paper,new four fifth-order fractional nonlinear equations are derived and investigated.The frac-tional terms are defined in the conformable sense and these equations are then solved using two effective methods... In this paper,new four fifth-order fractional nonlinear equations are derived and investigated.The frac-tional terms are defined in the conformable sense and these equations are then solved using two effective methods,namely,the sub-equation and the generalized Kudryashov methods.These methods were tested on the proposed models and succeeded in finding new solutions with different values of parameters.A graphical representation of some results is provided and proves the efficiency and applicability of the proposed methods for providing solutions with known physical behavior.These methods are good candi-dates for solving other similar problems in the future. 展开更多
关键词 Conformable derivative generalized Kudryashov method Sub-equation method riccati equation SOLITONS
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求一类Riccati微分方程通解的分项组合法 被引量:5
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作者 王桂花 王明建 《西安文理学院学报(自然科学版)》 2011年第2期46-48,共3页
讨论了一类Riccati微分方程的通解,得到了它可以使用分项组合法的充要条件,为寻求Riccati微分方程的通解提供了有效的方法,并给出了它的应用.
关键词 riccati微分方程 通解 分项组合法 充要条件
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修正Benjamin-Bona-Mahony方程的精确行波解
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作者 杨春飞 刘小华 《内蒙古师范大学学报(自然科学版)》 CAS 2024年第5期532-541,共10页
利用平面动力系统理论,研究修正Benjamin-Bona-Mahony (mBBM)方程行波解的存在性,得到不同参数条件下的相图和行波解的存在条件。运用广义Riccati辅助方程法给出mBBM方程的双曲解、三角解和有理函数解。并利用Maple软件,分析扭状孤波解... 利用平面动力系统理论,研究修正Benjamin-Bona-Mahony (mBBM)方程行波解的存在性,得到不同参数条件下的相图和行波解的存在条件。运用广义Riccati辅助方程法给出mBBM方程的双曲解、三角解和有理函数解。并利用Maple软件,分析扭状孤波解、周期解的性状,数值上验证了精确行波解的表达式。 展开更多
关键词 MBBM方程 解的存在性 广义riccati辅助方程法 行波解
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关于Riccati方程的几个性质及应用 被引量:2
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作者 肖氏武 《襄樊学院学报》 2001年第5期18-21,共4页
Riccati方程的解一般是不能用初等函数给出的. 文章给出了一般Riccati方程的几个性质并运用这些性质可将Riccati方程化简. 同时介绍了一类Riccati方程可积的条件,并进行了一定的推广, 得出了两个结论.
关键词 riccati方程 初等积分法 变量变换 通解 微分方程 分式线性函数
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Kaup-Kupershmidt方程的精确行波解
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作者 杨春飞 刘小华 《南华大学学报(自然科学版)》 2024年第1期66-71,共6页
利用扩展tanh函数法研究了Kaup-Kupershmidt方程的精确行波解,得到了该方程不同类型的显式行波解,包括孤立波解、指数函数解和三角函数周期解。利用Maple软件绘制了所得解在具体参数值下的3D图和2D图,并对解的性态进行分析得出了相应解... 利用扩展tanh函数法研究了Kaup-Kupershmidt方程的精确行波解,得到了该方程不同类型的显式行波解,包括孤立波解、指数函数解和三角函数周期解。利用Maple软件绘制了所得解在具体参数值下的3D图和2D图,并对解的性态进行分析得出了相应解的类型。 展开更多
关键词 Kaup-Kupershmit方程 扩展tanh函数法 广义riccati方程 行波解
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一类Riccati方程的解
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作者 高正晖 《衡阳师范学院学报》 2003年第3期13-14,共2页
本文用初等积分法,求出了一类特殊的Riccati方程y′=f(x)y2+g(x)y+h(x),若f(x)=Aexp[-∫g(x)dx],h(x)=Bexp[∫g(x)dx]通解的解析表达式。(1)当AB=m2时,y=mAtan(mx+C)e∫g(x)dx1+Ce2mx(2)当AB=-m2时,y=mAA1-Ce2mxe∫g(x)
关键词 riccati方程 初等积分 通解
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两类可积的Riccati型方程
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作者 张晓强 《重庆工学院学报》 2000年第4期76-77,共2页
利用适当的变量代换法 ,找到了两类可积的Riccati型方程的求解方法 ,并给出了通积分的表达式。
关键词 riccati型方程 变量代换法 通积分 求解方法
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