物理学报
物理學報
물이학보
2013年
10期
1-9
,共9页
第二种椭圆方程%Riccati方程%非线性发展方程%Riemann theta函数无穷序列解
第二種橢圓方程%Riccati方程%非線性髮展方程%Riemann theta函數無窮序列解
제이충타원방정%Riccati방정%비선성발전방정%Riemann theta함수무궁서렬해
the second kind of elliptic equation%Riccati equation%nonlinear evolution equation%Riemann theta function infinite sequence solution
为了构造非线性发展方程的复合型无穷序列精确解,获得了第二种椭圆方程的Riemann theta函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的B¨acklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,以mKdV方程为应用实例,构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta函数、Jacobi椭圆函数、双曲函数、三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解.
為瞭構造非線性髮展方程的複閤型無窮序列精確解,穫得瞭第二種橢圓方程的Riemann theta函數等幾種新解.在此基礎上,利用第二種橢圓方程與Riccati方程的B¨acklund變換和解的非線性疊加公式,藉助符號計算繫統Mathematica,以mKdV方程為應用實例,構造瞭該方程的複閤型無窮序列新精確解.這裏包括Riemann theta函數、Jacobi橢圓函數、雙麯函數、三角函數和有理函數,通過幾種形式構成的複閤型無窮序列新精確解.
위료구조비선성발전방정적복합형무궁서렬정학해,획득료제이충타원방정적Riemann theta함수등궤충신해.재차기출상,이용제이충타원방정여Riccati방정적B¨acklund변환화해적비선성첩가공식,차조부호계산계통Mathematica,이mKdV방정위응용실례,구조료해방정적복합형무궁서렬신정학해.저리포괄Riemann theta함수、Jacobi타원함수、쌍곡함수、삼각함수화유리함수,통과궤충형식구성적복합형무궁서렬신정학해.
@@@@Riemann theta function and other several kinds of new solutions to the second kind of elliptic equation are obtained to construct the infinite sequence complexiton solutions of nonlinear evolution equations. Based on this, applying B¨acklund transformation and nonlinear superposition formula of the solutions to the second kind of elliptic equation and Riccati equation, mKdV equation is chosen as an example to seek infinite sequence new complexiton solutions with the help of symbolic computation system Mathematica, which are composed of Riemann theta function, Jacobi elliptic function, hyperbolic function, triangular function and rational function in several forms.
