| 微扰Burgers-KdV方程的孤子解 |
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| 引用本文： | 海文华,肖奕. 微扰Burgers-KdV方程的孤子解[J]. 物理学报, 1996, 45(4): 587-594 |
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| 作者姓名： | 海文华 肖奕 |
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| 作者单位： | (1)湖南教育学院物理系,长沙410012;中国高等科学技术中心(世界实验室),北京100080; (2)华中理工大学物理系,武汉430074 |
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| 基金项目： | 国家自然科学基金;湖南省自然科学基金资助的课题 |
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| 摘 要： | 对于一个其耗散项可看作微扰的Burgers-KdV(B-KdV)方程ut+uux+βuxxx=εuxx,|ε|?1,考虑一级近似和行波情形,建立一套求通解的直接扰动方法,利用零级方程的单孤子解,获得一级方程的孤子型通解,它包含任意多个不同的孤子解,每个孤子解分别描述一个位于半无限空间的孤子阵列,分析表明,耗散使得“亮孤子”变矮变窄,“暗孤子”变浅变窄.关键词：
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| 关 键 词： | KdV方程 孤子解 微扰 非线性方程 孤波 |
| 收稿时间： | 1995-04-11 |
SOLITON SOLUTIONS OF PERIURBED BURGERS-KdV EQUATION |
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| HAI WEN-HUA and XIAO YI. SOLITON SOLUTIONS OF PERIURBED BURGERS-KdV EQUATION[J]. Acta Physica Sinica, 1996, 45(4): 587-594 |
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| Authors: | HAI WEN-HUA and XIAO YI |
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| Abstract: | In this paper , we have studied a perturbed Burgers-Korteweg-de Vries equation ut+uux+βuxxx=εuxx,|ε|?1, Under first order approximation and travelling wave case, the direct perturba-tion method to find the general solution is established. By means of the single soliton solution of the zeroth order equation we have obtained the general soliton solution of the first order equation. It con-tains many diferent soliton solutions and any one of them describes an array of solitons in semi-infinite space. The analyses show that the dissipation e makes the bright soliton the lower and narrower and the dark soliton the shallower and narrower than unperturbed KdV soliton.
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