| 寻求孤子方程新的精确行波解的方法 |
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| 引用本文： | 韩琳,冯滨鲁. 寻求孤子方程新的精确行波解的方法[J]. 潍坊学院学报, 2009, 9(6): 61-67 |
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| 作者姓名： | 韩琳 冯滨鲁 |
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| 作者单位： | 1. 辽宁师范大学,辽宁,大连,116029
2. 潍坊学院,山东,潍坊,261061 |
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| 基金项目： | 国家自然科学基金，上海曙光跟踪课题 |
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| 摘 要： | 提出了寻求孤子方程（组）的孤波解的一类新方法,其形式为有限对数的Laurent展式,其辅助方程为常系数的二阶常微分方程;结合齐次平衡法与微分方程的特征多项式,获得了KdV方程、混合KdV-MKdV方程及（2＋1）维KP方程的精确孤波解,其中包含周期波解;利用本文提出的方法,可寻求其它孤子方程的精确解,因此该方法具有普遍应用性。
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| 关 键 词： | 齐次平衡法 KdV方程 行波解 |
New Method of Finding New Travlling Wave Solutions to the Solitary Equation |
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| HAN Lin,FENG Bin-lu. New Method of Finding New Travlling Wave Solutions to the Solitary Equation[J]. Journal of Weifang University, 2009, 9(6): 61-67 |
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| Authors: | HAN Lin FENG Bin-lu |
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| Affiliation: | HAN Lin,FENG Bin-lu (1.Liaoning Normal University,Dalian 116029,China;2.Weifang University,Weifang 261061,China) |
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| Abstract: | In this paper,we propose new method of finding new travlling wave solutions to the solitary equation,the formal solution is assumed as finite logarithm Laurent expansion,where the auxiliary equation is the second order ordinary differential equation with constant coefficient.By employing the homogeneous balance method and the characteristic polynomial of ordinary differential equation,we have obtained the exact travlling wave solutions to the KdV equation,the combined KdV-MKdV equation and（2＋1）dimensional KP equation,which contain the cyclic wave solutions.This method can be applied to other nonlinear evolution equations in soliton theory.Therefore this method has the universal utility. |
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| Keywords: | homogeneous balance method Kdv equation travlling wave solution |
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