A new integrable two-component system with cubic nonlinearity

Authors

Junfeng Song, Northwest University
Changzheng Qu, Shaanxi Normal University
Zhijun Qiao, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

6-5-2011

Abstract

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(u2x−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.

Comments

© 2011 American Institute of Physics. Original published version available at https://doi.org/10.1063/1.3530865

Recommended Citation

Song, Junfeng, Changzheng Qu, and Zhijun Qiao. 2011. “A New Integrable Two-Component System with Cubic Nonlinearity.” Journal of Mathematical Physics 52 (1): 013503. https://doi.org/10.1063/1.3530865.

Publication Title

Journal of Mathematical Physics

DOI

10.1063/1.3530865