The Boussinesq equation simulates weakly nonlinear and long wave approximation that can be used in water waves, coastal engineering, and numerical models for water wave simulation in harbors and shallow seas. In this article, the sine-Gordon expansion (SGE) approach and the generalized Kudryashov (GK) scheme are used to establish broad-spectral solutions including unknown parameters and typical analytical solutions are recovered as a special case. The well-known bell-shape soliton, kink, singular kink, compacton, contracted bell-shape soliton, periodic soliton, anti-bell shape soliton, and other shape solitons are retrieved for the definite value of these constraints. The 3D and contour plots of some of the results obtained are sketched by assigning individual values of the parameter and analyzed the dynamical behavior of the waves. Furthermore, the compatibility of the two approaches has been compared and examined the efficiency to ascertain soliton solutions.

Boussinesq方程可模拟弱非线性和长波近似，可用于水波，海岸工程以及港口和浅海中水波模拟的数值模型。在本文中，使用正弦-Gordon展开（SGE）方法和广义Kudryashov（GK）方案来建立 作为特殊情况，将恢复包括未知参数和典型分析解决方案在内的广谱解决方案。对于这些约束的确定值，检索到了著名的钟形孤子，扭结，奇异扭结，紧凑子，收缩的钟形孤子，周期孤子，反钟形孤子和其他形状孤子。通过分配参数的各个值来绘制获得的某些结果的3D和轮廓图，并分析波浪的动态行为。此外，已经比较了两种方法的兼容性，并检查了确定孤子解决方案的效率。