Special Session 83: 

On the exact solutions of nonlocal Boussinesq equation

Emrullah Yasar
Uludag University
Turkey
Co-Author(s):    
Abstract:
\begin{document} \begin{center} On the exact solutions of nonlocal Boussinesq equation \end{center} This study devotes to the (1+1)-dimensional integrable system known as the nonlocal Boussinesq equation. This model emerges as a compatibility condition for a linear system associated with the bilinear representation of Kaup`s higher-order wave equation. The nonlocal symmetries for the nlBq equation are obtained with the truncated Painleve approach. Based on the truncated Painleve expansion, the nonlocal symmetry and Backlund transformation of this equation are extracted. The nonlocal symmetries can be localized to the Lie point symmetries by help of new auxiliary dependent variables. The corresponding Lie symmetry transformations related to the nonlocal symmetries are derived. The considered model is demonstrated to be consistent Riccati solvable. Some new exact solutions including the two-solitary-wave fusion solutions, single soliton solutions and interaction wave solutions are also revealed. \end{document}