We first derive a Darboux transformation for a (2+ 1)-extension of Burgers equation. Then we consider theLie symmetries, symmetry algebra, and symmetry reductions of the equation, and use symmetry reductions to obtain...We first derive a Darboux transformation for a (2+ 1)-extension of Burgers equation. Then we consider theLie symmetries, symmetry algebra, and symmetry reductions of the equation, and use symmetry reductions to obtaingroup-invariant solutions to the equation.展开更多
Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e'...Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e') analysis,the most generalized Painlev(e') integrable(2+1)-dimensional integrable Burgers systems are obtained.Some exact solutions of the generalized Burgers system are obtained via variable separation approach.展开更多
A 严济慈祖籍浙江,于1901年1月23日出生在浙江省东阳县下湖严村一个普通的农家。下湖严村是一个仅有30多户人家的小山村,耕地面积少得可怜,非常贫困,然而却盛行读书的风气。严济慈自幼聪颖、勤奋好学,在全家人的全力资助下,他从小学升...A 严济慈祖籍浙江,于1901年1月23日出生在浙江省东阳县下湖严村一个普通的农家。下湖严村是一个仅有30多户人家的小山村,耕地面积少得可怜,非常贫困,然而却盛行读书的风气。严济慈自幼聪颖、勤奋好学,在全家人的全力资助下,他从小学升入中学,后又考入南京高等师范专科学校。展开更多
In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obt...In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.展开更多
From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the ...From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.展开更多
A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wav...A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.展开更多
基金supported by the Scientific Research Foundation of Yunnan Provincial Education Department(2018JS752)the National Natural Science Foundation of China(11801240)
文摘We first derive a Darboux transformation for a (2+ 1)-extension of Burgers equation. Then we consider theLie symmetries, symmetry algebra, and symmetry reductions of the equation, and use symmetry reductions to obtaingroup-invariant solutions to the equation.
文摘Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e') analysis,the most generalized Painlev(e') integrable(2+1)-dimensional integrable Burgers systems are obtained.Some exact solutions of the generalized Burgers system are obtained via variable separation approach.
文摘In this paper we consider the construction of solutions to the Cauchy problem of Burgers' equations ut-γ△u+u·u=0,t∈R^+,x∈R^3(1) u(0,x)=u0(x),x∈R^3(2)
文摘In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
文摘From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.
文摘A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.
