查看“︁本杰明-博纳-马奥尼方程”︁的源代码

'''本杰明 - 博纳 - 马奥尼方程'''(Benjamin–Bona–Mahony equation)是本杰明、博纳和马奥尼在1972年模拟[[流体力学]]中小振幅长波的非线性偏微分方程：

:<math>u_t+u_x+uu_x-u_{xxt}=0.\,</math>

==行波解==
[[File:BBM animation.gif|thumb|Benjamin–Bona–Mahony equation  animation]]
BBM 方程有行波解.<ref>{{harvs | author1-link=Brooke Benjamin | last=Benjamin | author2-link=Jerry L. Bona | last2= Bona | author3-link=John Joseph Mahony | last3= Mahony | year=1972 | txt=yes }}</ref>


<math>u(x, t) = -\frac{8*_C2^2*_C3+_C3+_C2}{_C2}+12*_C2*_C3*tanh(_C1+_C2*x+_C3*t)^2</math>

参数：  _C3 = 5, _C2 =5，, _C1 = 5；
{{Gallery
|width=250
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|File:Benjamin–Bona–Mahony equation traveling wave plot5.gif|
|File:Benjamin–Bona–Mahony equation traveling wave plot2.gif|
|File:Benjamin–Bona–Mahony equation traveling wave plot11.gif|
|File:Benjamin–Bona–Mahony equation traveling wave plot10.gif|
|File:Benjamin–Bona–Mahony equation traveling wave Jacobi plot5.gif|
|File:Benjamin–Bona–Mahony equation traveling wave Jacobi plot7.gif|
|File:Benjamin–Bona–Mahony equation traveling wave Jacobi plot20.gif|
|File:Benjamin–Bona–Mahony equation traveling wave Jacobi plot2.gif|
|File:Benjamin–Bona–Mahony equation traveling wave Jacobi plot18.gif|
|File:Benjaminin Bona Mahony equation traveling wave plot24.gif|
|File:Benjaminin Bona Mahony equation traveling wave plot25.gif|
|File:Benjaminin Bona Mahony equation traveling wave plot27.gif|
}}


==参考文献==
<references/>
*{{citation|doi=10.1016/0362-546X(85)90023-9|mr=0799889
|last=Avrin|first=Joel|last2= Goldstein|first2= Jerome A.
|title=Global existence for the Benjamin–Bona–Mahony equation in arbitrary dimensions.
|journal=Nonlinear Anal.|volume= 9 |year=1985|issue= 8|pages= 861–865 }}
*{{citation | title=Model Equations for Long Waves in Nonlinear Dispersive Systems
| first1= T. B. |last1=Benjamin |authorlink1=Brooke Benjamin |first2= J. L.|last2= Bona | authorlink2=Jerry L. Bona | first3=J. J.|last3= Mahony
| journal=Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences | volume= 272 | issue= 1220 | year= 1972 | pages= 47–78
| jstor= 74079|ISSN =0962-8428 | doi=10.1098/rsta.1972.0032 | bibcode=1972RSPTA.272...47B}}
*{{citation|mr=0977062
|last=Zwillinger|first= Daniel
|title=Handbook of differential equations|publisher= Academic Press, Inc.|place= Boston, MA|edition=3rd|year= 1998|ISBN=  978-0-12-784396-4|pages=174, 176}} 
{{非线性偏微分方程}}
[[category:非线性偏微分方程]]
[[Category:流体力学中的方程]]