查看“︁戴维-斯图尔森方程组”︁的源代码

'''戴维-斯图尔森方程组'''(Davey–Stewartson equation)是Davey、Stewartson在1974年用以模拟水面波包传播的非线性偏微分方程<ref name=davy>Davey Stewardson</ref>：

:<math>i u_t + c_0 u_{xx} + u_{yy} = c_1 |u|^2 u + c_2 u \phi_x,\,</math>

:<math>\phi_{xx} + c_3 \phi_{yy} = ( |u|^2 )_x.\,</math>

==行波解==
:<math> u(x, y, t) = 0, v(x, y) = _C6+_C7*cot(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)  </math>
:<math>  u(x, y, t) = 0, v(x, y) = _C6+_C7*coth(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t) </math>
:<math>  u(x, y, t) = 0, v(x, y) = _C6+_C7*tan(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t) </math>
:<math> u(x, y, t) = 0, v(x, y) = _C6+_C7*tanh(_C2+_C3*x+_C3*y/\sqrt(-_C1)+_C5*t)  </math>
:<math> u(x, y, t) = 0, v(x, y) = _C6+_C7*arcsinh(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)+_C8*arcsinh(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)^2  </math>
:<math> u(x, y, t) = 0, v(x, y) = _C6+_C7*cos(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)+_C8*cos(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)^2  </math>
:<math> u(x, y, t) = 0, v(x, y) = _C6+_C7*cosh(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)+_C8*cosh(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)^2  </math>
:<math> u(x, y, t) = 0, v(x, y) = _C6+_C7*cot(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)+_C9*cot(_C2+_C3*x-_C3*y/\sqrt(-_C1)+_C5*t)^3  </math>
:<math> u(x, y, t) = 0, v(x, y) = _C7+_C8*JacobiCN(_C3+_C4*x-_C4*y/\sqrt(-_C1)+_C6*t, _C2)+_C10*JacobiCN(_C3+_C4*x-_C4*y/\sqrt(-_C1)+_C6*t, _C2)^3  </math>
:<math>  {u(x, y, t) = 0, v(x, y) = _C7+_C8*JacobiDN(_C3+_C4*x-_C4*y/\sqrt(-_C1)+_C6*t, _C2)+_C10*JacobiDN(_C3+_C4*x-_C4*y/\sqrt(-_C1)+_C6*t, _C2)^3} </math>
:<math> u(x, y, t) = 0, v(x, y) = _C7+_C8*JacobiND(_C3+_C4*x-_C4*y/\sqrt(-_C1)+_C6*t, _C2)+_C10*JacobiND(_C3+_C4*x-_C4*y/\sqrt(-_C1)+_C6*t, _C2)^3  </math>
:<math>  u(x, y, t) = 0, v(x, y) = _C7+_C8*JacobiNS(_C3+_C4*x+_C4*y/\sqrt(-_C1)+_C6*t, _C2)+_C10*JacobiNS(_C3+_C4*x+_C4*y/\sqrt(-_C1)+_C6*t, _C2)^3 </math>

==行波图==
{|
|[[File:Davey-Stewardson equation traveling wave plot 1.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 2.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 3.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 4.gif|thumb|戴维-斯图尔森方程组行波图]]
|}
{|
|[[File:Davey-Stewardson equation traveling wave plot 5.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 6.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 7.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 8.gif|thumb|戴维-斯图尔森方程组行波图]]
|}
{|
|[[File:Davey-Stewardson equation traveling wave plot 9.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 10.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 11.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 12.gif|thumb|戴维-斯图尔森方程组行波图]]
|}
{|
|[[File:Davey-Stewardson equation traveling wave plot 13.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 14.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 15.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 16.gif|thumb|戴维-斯图尔森方程组行波图]]
|}
{|
|[[File:Davey-Stewardson equation traveling wave plot 17.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 18.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 19.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 20.gif|thumb|戴维-斯图尔森方程组行波图]]
|}
{|
|[[File:Davey-Stewardson equation traveling wave plot 21.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 22.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 23.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 24.gif|thumb|戴维-斯图尔森方程组行波图]]
|}
{|
|[[File:Davey-Stewardson equation traveling wave plot 25.gif|thumb|戴维-斯图尔森方程组行波图]]
|[[File:Davey-Stewardson equation traveling wave plot 26.gif|thumb|戴维-斯图尔森方程组行波图]]
|}

==相關條目==
*[[扎哈羅夫-舒爾曼系統]]

==参考文献==
<references/>
*{{citation|<!--unused_data=Solitons in science and engineering: theory and applications.-->|mr=1368226
|last=Boiti|first= M.|last2= Martina|first2= L.|last3= Pempinelli|first3= F.
|title=Multidimensional localized solitons
|journal=Chaos Solitons Fractals |volume=5 |year=1995|issue=12|pages= 2377–2417
|doi=10.1016/0960-0779(94)E0106-Y |bibcode = 1995CSF.....5.2377B }} 
*{{citation|last=Davey|first= A.|authorlink2=Keith Stewartson|last2=Stewartson |first2=K.|title=On three dimensional packets of surface waves|journal= Proc. R. Soc. A |volume=338 |year=1974|issue=1613|pages= 101–110
|doi=10.1098/rspa.1974.0076|bibcode = 1974RSPSA.338..101D }}
*{{citation|editor1-first=David H.|editor1-last= Sattinger|editor2-first= C. A. |editor2-last=Tracy |editor3-first=S. |editor3-last= Venakides |title=Inverse Scattering and Applications |year= 1991
|mr=1135850 |series= Contemporary Mathematics |volume= 122 |publisher= American Mathematical Society |place= Providence, RI |isbn=0-8218-5129-2 }}
{{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]]