Nonlocal Symmetries and Consistent Riccati Expansions of the (2+1)-Dimensional Dispersive Long Wave Equation

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

来源：Zeitschrift fur Naturforschung Section A-A Journal of Physical Sciences, 2017, 72(5): 425-431.

DOI：10.1515/zna-2017-0012

• Nonlocal Symmetry
• Soliton-Cnoidal Wave Interaction Solution
• Symmetry Group Transformation
• The (2+1)-Dimensional Dispersive Long Water-Wave Equation
• Truncated Painleve Expansion

In this article, the (2+1)-dimensional dispersive long wave equation (DLWE) is investigated, which is derived in the context of a water wave propagating in narrow infinitely long channels of finite constant depth. By using of the truncated Painleve expansion, we construct its nonlocal symmetry and Backlund transformation. After implanting the equation into an enlarged one, then the residual symmetry is localised. Meanwhile, the symmetry group transformation can be computed from the prolonged system. Furthermore, the equation is verified to be consistent Riccati expansion (CRE) solvable. Outing from the CRE, the soliton-cnoidal wave interaction solution in terms of Jacobi elliptic functions and the third type of incomplete elliptic integral are studied, respectively.

• 出版日期2017-5
• 单位中国矿业大学（北京）