Painlevé Test and Exact Solutions for (1 + 1)-Dimensional Generalized Broer–Kaup Equations

In this paper, the Painlevé integrable property of (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, Bäcklund transformations for gBK are derived by using truncation. Based on a special case transformations, linearized into heat conduction equation. Inspired reduced Burgers Starting from linear equation, two forms N-soliton solutions and rational with singularity condition constructed. addition, conditions equation obtained considering non-uniqueness generality resonance function embedded test. order to understand nonlinear dynamic evolution dominated equations, some exact solutions, including one-soliton two-soliton three-soliton pairs shown three-dimensional images. This paper shows that when test deals coupled highest negative power variables should be comprehensively considered in leading term analysis rather than formal balance between highest-order derivative term.