Application of the tanh function method in deriving abundant analytical wave solutions to the high-order Boussinesq–Burgers equation

Guoliang He and Zhiwei Zhao

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 633-649

Abstract: By applying traveling wave transformation techniques, the higher-order Boussinesq–Burgers (HOBB) equation is reduced to an ordinary differential equation. Through systematic implementation of the tanh function method and three kinds of different extended formulations, some exact solutions to the HOBB equation are successfully obtained, including the periodic solutions, singular soliton solutions and the Jacobian elliptic function solutions. Then, the dynamic evolution characteristics of these solutions are analyzed through three-dimensional graphical representations with carefully selected parameter configurations. This investigation not only extends the solution space for the HOBB equation, but also provides new insights into nonlinear wave propagation mechanisms.

Keywords: Higher-order Boussinesq–Burgers equation; Explicit solutions; Tanh-function method; Extended tanh-function method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:633-649

DOI: 10.1016/j.matcom.2025.07.060

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