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应用 Bernoulli 型简单方程求（2＋1）维KP 方程的精确行波解
  • ISSN号：1000-2537
  • 期刊名称：《湖南师范大学自然科学学报》
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]内蒙古工业大学理学院,中国呼和浩特010051, [2]中国矿业大学理学院,中国徐州221116
  • 相关基金：国家自然科学基金资助项目（11071159）;内蒙古高等学校研究重点项目（NJ2214053）
作者： 和玲超[1], 庞晶[1], 赵忠龙[2]
关键词： 简单方程法, (2+1)维KP方程, 精确行波解, method of simplest equation, （2＋1）-dimensional KP equation, exact traveling-wave solutions
中文摘要：

利用行波变换把（2＋1）维KP方程化成常微分方程，再运用简单方程法求解（2＋1）维KP方程的行波解。文中选取Bernoulli方程为简单方程。将由KP方程所化成的常微分方程分成两部分：一部分包含导数项，另一部分为方程其他部分。然后，平衡最高次幂的非线性项所产生的最高次数和最高阶导数项所产生的最高项的次数，得到平衡方程，确定解的形式。最后解得（2＋1）维KP方程的行波解。

英文摘要：

Traveling-wave coordinate is used for transforming KP equation to a nonlinear ordinary differential equation .The traveling-wave solutions of KP equation are obtained by the method of the simplest equation when the simplest equation is the Bernoulli equation .The nonlinear ordinary equation is divided into two parts：part A con-tains the derivatives, and part B contains the rest of the equation .Then,balancing the highest powers of the polyno-mials for the parts A and B and a balance equation is obtained which depends on the kind of the simplest equation , the form of solution is determined .Finally, the new traveling-wave solutions of the KP equation are obtained .

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期刊信息
  • 《湖南师范大学自然科学学报》
  • 中国科技核心期刊
  • 主管单位:湖南师范大学
  • 主办单位:湖南师范大学
  • 主编：杨春明
  • 地址：湖南长沙岳麓山湖南师范大学期刊社
  • 邮编：410081
  • 邮箱：xbz@hunnu.edu.cn
  • 电话：0731-8872473
  • 国际标准刊号：ISSN：1000-2537
  • 国内统一刊号：ISSN：43-1065/N
  • 邮发代号:42-96
  • 获奖情况:
  • 全国优秀科技期刊一等奖
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  • 被引量:4771