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摘要: 采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
Abstract: The homogeneous balance method for constructing solitary wave solutions and soliton solutions is further developed on obtaining quasi-solution by using step-by- step principle.The main advantage of the extended approach is to avoid the probl em of “intermediate expression swell”.The effectiveness of the method is demon strated by application to the generalized Boussinesq equation and the bidirectio nal Kaup-Kupershmidt equation.The one-soliton,two-soliton and three-soliton solutions with multipe collisions are derived for these two equations with the assistance of Maple.
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