几类非线性数学物理方程精确解的符号计算  

Symbolic computation of new exact solutions for some nonlinear equations in mathematical physics

作　　者：周凯[1] 杨军 马立媛 沈守枫[1] ZHOU Kai;YANG Jun;MA Li-yuan;SHEN Shou-feng(Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China;Department of Mathematics,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]浙江工业大学应用数学系,浙江杭州310023 [2]上海交通大学数学系,上海200240

出　　处：《高校应用数学学报（A辑）》2020年第2期223-234,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11701510)。

摘　　要：利用符号计算软件Maple,研究了几类非线性数学物理方程的精确解.由Hirota双线性方法构造了可积非局部离散mKdV方程的N-孤子解的显式表达式,且对于2-孤子解,分析了渐近行为.从Jacobi椭圆函数出发,得到了多分量Klein-Gordon方程和长波-短波方程的行波解.当模m→1,这些解退化为相应的双曲函数解,如钟型孤子解.In this paper,new exact solutions of some nonlinear equations in mathematical physics are constructed by using the symbolic computation software Maple.Firstly,the two-soliton solution for an integrable nonlocal discrete m KdV equation is obtained via the Hirota’s bilinear method,and the asymptotic behavior is analyzed.A kind of explicit expression for the N-soliton solution also is given.Secondly,abundant families of travelling wave solutions of the multicomponent Klein-Gordon system and long wave-short wave system are obtained directly by means of the Jacobi elliptic functions.When the modulus m→1,those solutions degenerate as the corresponding hyperbolic function solutions including the bell-type soliton solution.

关 键 词：精确解 非局部离散m KdV方程 KLEIN-GORDON方程 长波-短波方程 符号计算 

分 类 号：O175.14[理学—数学]