In this work, analytical approximate progressive wave solutions for the generalized form of the nonplanar KdV-Burgers (KdV-B) and mKdV-Burgers (mKdV-B) equations are presented and the results are discussed. Motivated with the exact solutions of the planar KdV-B and mKdV-B equations, the weighted residual method is applied to propose analytical approximate solutions for the generalized form of the nonplanar KdV-B and mKdV-B equations. The structure of the KdV-B equation assumes a solitary wave type of solution, whereas the mKdV-B equation assumes a shock wave type of solution. The analytical approximate progressive wave solutions for the cylindrical(spherical) KdV-B and mKdV-B equations are obtained as some special cases and compared with numerical solutions and the results are depicted on 2D and 3D figures. The results revealed that both solutions are in good agreement. The advantage of the present method is that it is rather simple as compared to the inverse scattering method and gives the same results with the perturbative inverse scattering technique. Moreover, the present analytical solutions allow readers to carry out physical parametric studies on the behavior of the solution. In addition to the present solutions are defined overall the problem domain not only over the grid points, as well as the solution calculation has less CPU time-consuming and round-off error.

在这项工作中，提出了非平面KdV-Burgers（KdV-B）和mKdV-Burgers（mKdV-B）方程的广义形式的解析近似渐进波解，并对结果进行了讨论。根据平面KdV-B和mKdV-B方程的精确解，采用加权残差法为非平面KdV-B和mKdV-B方程的广义形式提出解析近似解。KdV-B方程的结构假定为孤立波类型的解，而mKdV-B方程的结构假定为激波类型的解。在某些特殊情况下，获得了圆柱（球形）KdV-B和mKdV-B方程的解析近似渐进波解，并与数值解进行了比较，并在2D和3D图上描绘了结果。结果表明，两种解决方案都非常吻合。本方法的优点是与逆散​​射方法相比相当简单，并且与摄动逆散射技术给出相同的结果。此外，本分析解决方案允许读者对解决方案的行为进行物理参数研究。除了本解决方案之外，总体上还定义了问题领域，不仅涉及网格点，而且解决方案计算的CPU耗时和舍入误差均较小。本分析解决方案使读者可以对解决方案的行为进行物理参数研究。除了本解决方案之外，总体上不仅在网格点上定义了问题域，而且解决方案计算具有更少的CPU耗时和舍入误差。本分析解决方案使读者可以对解决方案的行为进行物理参数研究。除了本解决方案之外，总体上还定义了问题领域，不仅涉及网格点，而且解决方案计算的CPU耗时和舍入误差均较小。