Nonlocal symmetry and consistent Riccati expansion integrability of the (1+1)-dimensional integrable nonlinear dispersive-wave system

作者：Feng, Lian-Li; Tian, Shou-Fu^*; Wang, Xiu-Bin; Zhang, Tian-Tian^*

来源：Waves in Random and Complex Media, 2017, 27(3): 571-586.

DOI：10.1080/17455030.2016.1278286

• PARTIAL-DIFFERENTIAL-EQUATIONS
• KADOMTSEV-PETVIASHVILI EQUATION
• CLASSICAL BOUSSINESQ SYSTEM
• MULTIPLE-SOLITON-SOLUTIONS
• DARBOUX TRANSFORMATIONS
• RATIONAL CHARACTERISTICS
• EXPLICIT SOLUTIONS
• LIE SYMMETRIES
• WATER

Under investigation in this paper is nonlocal symmetry, consistent Riccati expansion (CRE) integrability of the (1+1)-dimensional integrable nonlinear dispersive-wave system, which can be used to describes a bidirectional soliton for wave propagation. We construct the Backlund transformation and consider the truncated Painleve expansion of the system. It's Schwarzian form is derived, whose nonlocal symmetry is localized to provide the corresponding nonlocal group. Furthermore, we verify that the system is solvable via the CRE. Based on the CRE, we further present its soliton-cnoidal wave interaction solution in terms of Jacobi elliptic functions and the third type of incomplete elliptic integral.

• 出版日期2017
• 单位中国矿业大学（北京）