A new integrable two-component system with cubic nonlinearity

In this paper, a new integrable two-component system, \documentclass[12pt]{minimal}\begin{document}$m_t=[m(u_xv_x-uv+uv_x\break -u_x v)]_x, n_t=[n(u_xv_x\,{-}\,uv\,{+}\,uv_x\,{-}\,u_x v)]_x,$\end{document}mt=[m(uxvx−uv+uvx−uxv)]x,nt=[n(uxvx−uv+uvx−uxv)]x, where \documentclass[12pt]{minimal}\begin{document}$m\,{=}\,u\,{-}\,u_{xx}$\end{document}m=u−uxx and \documentclass[12pt]{minimal}\begin{document}$n=v-v_{xx}$\end{document}n=v−vxx, is proposed. Our system is a generalized version of the integrable system \documentclass[12pt]{minimal}\begin{document}$m_t=[m(u_x^2\break-u^2)]_x,$\end{document}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.