A new integrable two-component system with cubic nonlinearity
A new integrable two-component system with cubic nonlinearity
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DOI：
10.1063/1.3530865
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发表时间：
2011-01
影响因子：
1.3
通讯作者：
Junfeng Song;Changzheng Qu;Zhijun Qiao
中科院分区：
文献类型：
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作者：
Junfeng Song;Changzheng Qu;Zhijun Qiao
本文提出了一个新的可积两分量系统mt=[m（uxvx−uv+uvx−uxv）]x，nt=[n（uxvx−uv+uvx−uxv）]x，其中m=u−uxx，n=v−vxx.我们的系统是可积系统mt=[m（ux 2-u2）]x的推广版本，其被乔[J. Math. Phys. 47，112701（2006）]证明具有尖点解（cuspon）和W/M形孤子解。证明了新系统不仅在Lax-对意义下是可积的，而且在几何意义下也是可积的，即它描述了伪球面。因此，无穷多个守恒定律是通过递归关系导出的。此外，还得到了尖点孤子和W/M型孤子的精确解。
In this paper, a new integrable two-component system, mt=[m(uxvx−uv+uvx−uxv)]x,nt=[n(uxvx−uv+uvx−uxv)]x, where m=u−uxx and n=v−vxx, is proposed. Our system is a generalized version of the integrable system mt=[m(ux2−u2)]x, which was shown having cusped solution (cuspon) and W/M-shape soliton solutions by Qiao [J. Math. Phys. 47, 112701 (2006). The new system is proven integrable not only in the sense of Lax-pair but also in the sense of geometry, namely, it describes pseudospherical surfaces. Accordingly, infinitely many conservation laws are derived through recursion relations. Furthermore, exact solutions such as cuspons and W/M-shape solitons are also obtained.