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中文摘要：
在求非线性偏微分方程精确解的过程中两次使用了齐次平衡法（称为累次齐次平衡法），解决了齐次平衡法求解少的不足．从而改进了齐次平衡法．以高阶（2＋1）维Kadomtsev—Petviashvili方程和变异的Boussinesq方程为应用实例，说明使用累次齐次平衡法可以求得大量的精确解，其中许多解是新解或覆盖了其他方法所得的解、方法可应用于大量的非线性物理模型．
英文摘要：
The homogeneous balance method is applied twice and then improved to construct the exact traveling wave solutions of nonlinear partial differential equations （called the repeated homogeneous balance method）. As two illustrative equations, （2＋1）-dimensional Kadomtsev- Petviashvili equation and variant Boussinesq equations are investigated by the repeated homogeneous balance method, and a lot of their exact traveling wave solutions are obtained, in which many solutions are new and more general types of solutions. The repeated homogeneous balance method can be used to solve lots of nonlinear physical model.
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The repeated homogeneous balance method and its applications to nonlinear partical differential equa
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