| 一类非线性偏微分方程Baecklund变换的分类 |
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| 引用本文： | 杨瑜.一类非线性偏微分方程Baecklund变换的分类[J].曲阜师范大学学报,2010,36(1):49-54. |
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| 作者姓名： | 杨瑜 |
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| 作者单位： | 宿迁高等师范学校数学系,江苏省宿迁市223800 |
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| 摘 要： | 讨论了形如u_t=u_(xxx)+F(u,u_x)的非线性偏微分方程由可积系统{v_x=P(v,u,u_t,u_x,u_(xx)),v_t=Q(v,u,u_t,u_x,u_(xx_)定义的Baecklund变换u→v分类问题,给出光滑函数F,P和Q的显式表达式,得到函数F只能是如下形式F(u,u_x)=cu_x~3+F_1(u)u_x,其中c是常数,并且分3种情形确定光滑函数F和相应的函数P和Q.
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| 关 键 词： | 非线性偏微分方程 可积系统 Baecklund变换 |
On Baecklund Transformations for a Class of Nonlinear Partial Differential Equation |
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| YANGYu.On Baecklund Transformations for a Class of Nonlinear Partial Differential Equation[J].Journal of Qufu Normal University(Natural Science),2010,36(1):49-54. |
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| Authors: | YANGYu |
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| Institution: | YANG+Yu(Department+of+Mathematics,Suqian+Higher+Normal+School,223800,Suqian,Jiangsu,PRC) |
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| Abstract: | We classify nonlinear partial differential equations of the form ut=uxxx+F(u,ux) which possess Baecklund transformations defined via associated integrable systems vx=P(v,u,ut,ux,uxx),vt=Q(v,u,ut,ux,uxx).We determine such smooth functions F,P and Q.Our results show that the function F can only be of the formF(u,ux)=cu3x+F1(u)ux,where c is a constant and F1 is a smooth function. |
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| Keywords: | nonlinear partial differential equation integrable system Baecklund transformation |
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