Sinh-G{<$}rdon方程行波解的表示与分类
Representations and classification of traveling wave solutions to Sinh-G{ö}rdon equation
摘要：
定义了原子解和组合解两个概念。给出了Sinh-G{rdon方程所有单行波原子解的分类，并讨论了解的定性性质.特别指出了动力系统方法直观地导出的一些定性性质是不正确的。最后，我们证明了Sinh-G{<$}rdon方程的解包含了文[Fu Z T et al，Commu.在Theor。Phys.（北京）2006 45 55]。通过一个例子，给出了雅可比椭圆函数的一些新的恒等式。
英文摘要：
Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{ö}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{ö}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.
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