物理学报
物理學報
물이학보
2013年
7期
8-14
,共7页
G′(ξ) G(ξ) 展开法%非线性叠加公式%非线性发展方程%复合型类孤子新解
G′(ξ) G(ξ) 展開法%非線性疊加公式%非線性髮展方程%複閤型類孤子新解
G′(ξ) G(ξ) 전개법%비선성첩가공식%비선성발전방정%복합형류고자신해
the G′(ξ) G(ξ) expansion method%nonlinear superposition formula%nonlinear evolution equation%new com-plexion soliton-like solution
为了构造非线性发展方程的无穷序列复合型类孤子新解,进一步研究了 G′(ξ) G(ξ)展开法.首先,给出一种函数变换,把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题.然后,利用Riccati方程解的非线性叠加公式,获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解.在此基础上,借助符号计算系统Mathematica,构造了改进的(2+1)维色散水波系统和(2+1)维色散长波方程的无穷序列复合型类孤子新精确解.
為瞭構造非線性髮展方程的無窮序列複閤型類孤子新解,進一步研究瞭 G′(ξ) G(ξ)展開法.首先,給齣一種函數變換,把常繫數二階齊次線性常微分方程的求解問題轉化為一元二次方程和Riccati方程的求解問題.然後,利用Riccati方程解的非線性疊加公式,穫得瞭常繫數二階齊次線性常微分方程的無窮序列複閤型新解.在此基礎上,藉助符號計算繫統Mathematica,構造瞭改進的(2+1)維色散水波繫統和(2+1)維色散長波方程的無窮序列複閤型類孤子新精確解.
위료구조비선성발전방정적무궁서렬복합형류고자신해,진일보연구료 G′(ξ) G(ξ)전개법.수선,급출일충함수변환,파상계수이계제차선성상미분방정적구해문제전화위일원이차방정화Riccati방정적구해문제.연후,이용Riccati방정해적비선성첩가공식,획득료상계수이계제차선성상미분방정적무궁서렬복합형신해.재차기출상,차조부호계산계통Mathematica,구조료개진적(2+1)유색산수파계통화(2+1)유색산장파방정적무궁서렬복합형류고자신정학해.
The G′(ξ) G(ξ) expansion method is further studied for constructing new infinite sequence complexion soliton-like solutions of non-linear evolution equations. First, to solve a linear ordinary differential equation with constant coefficients of second order is changed into the solving of one unknown quadratic equation and Riccati equation by a function transformation. Then a nonlinear superposition formula of the solutions to Riccati equation is presented to seek new infinite sequence complexion solutions of a second order linear ordinary differential equation with constant coefficients. Based on this, the new infinite sequence complexion soliton-like solutions to (2+1)-dimensional modified dispersive water wave system and (2+1)-dimensional dispersive long-wave equation are obtained with the help of symbolic computation system Mathematica.
