A new integrable two-component system with cubic nonlinearity

作者：Song, Junfeng; Qu, Changzheng; Qiao, Zhijun^*

来源：Journal of Mathematical Physics, 2011, 52(1): 013503.

DOI：10.1063/1.3530865

• CAMASSA-HOLM EQUATION
• SHALLOW-WATER EQUATION
• GEODESIC-FLOW
• BLOW-UP
• PSEUDOSPHERICAL SURFACES
• DIFFEOMORPHISM GROUP
• EVOLUTION-EQUATIONS
• WAVES
• TRAJECTORIES
• SOLITONS

In this paper, a new integrable two-component system, m(t) = [m(u(x)v(x) - uv + uv(x) - u(x)v)](x), n(t) = [n(u(x)v(x) - uv + uv(x) - u(x)v)](x), where m = u - u(xx) and n = v - v(xx), is proposed. Our system is a generalized version of the integrable system m(t) = [m(u(x)(2) -u(2))](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.

• 出版日期2011-1
• 单位陕西师范大学; 西北大学