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高校应用数学学报
高校应用数学学报  2020, Vol. 35 Issue (2): 223-234    
    
几类非线性数学物理方程精确解的符号计算
周 凯, 杨 军, 马立媛, 沈守枫
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
Symbolic computation of new exact solutions for some nonlinear equations in mathematical physics
ZHOU Kai, YANG Jun, MA Li-yuan, SHEN Shou-feng
1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023;
2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240
 全文: PDF(5079 KB)  
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.
关键词： 精确解;  非局部离散mKdV方程;  Klein-Gordon方程;  长波-短波方程;  符号计算    
Abstract: 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 mKdV 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.
Key words: exact solution    nonlocal discrete mKdV equation    Klein-Gordon system    long waveshort wave system    symbolic computation
出版日期: 2020-07-07
CLC:  O175.14  
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周 凯
杨 军
马立媛
沈守枫

引用本文:

周 凯, 杨 军, 马立媛, 沈守枫. 几类非线性数学物理方程精确解的符号计算[J]. 高校应用数学学报, 2020, 35(2): 223-234.

ZHOU Kai, YANG Jun, MA Li-yuan, SHEN Shou-feng. Symbolic computation of new exact solutions for some nonlinear equations in mathematical physics. Applied Mathematics A Journal of Chinese Universities, 2020, 35(2): 223-234.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2020/V35/I2/223

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