"Modified KdV (mKdV) equation"의 두 판 사이의 차이
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| 6번째 줄: | 6번째 줄: | ||
u_t+6u^2u_x+u_{xxx}=0 | u_t+6u^2u_x+u_{xxx}=0 | ||
$$ | $$ | ||
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| + | ==$N$-solution solution== | ||
* $N$-solution solution | * $N$-solution solution | ||
$$ | $$ | ||
| 19번째 줄: | 21번째 줄: | ||
** M. Wadati and K. Ohkuma, J. Phys. Soc. Japan. 51,2029 (1982). | ** M. Wadati and K. Ohkuma, J. Phys. Soc. Japan. 51,2029 (1982). | ||
** M. Wadati, J. Phys. Soc. Japan.77, 074005 (2008) | ** M. Wadati, J. Phys. Soc. Japan.77, 074005 (2008) | ||
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| + | |||
| + | ==periodic solution== | ||
| + | * M. Wadati, J. Phys. Soc. Japan.77, 074005 (2008) | ||
| + | * M. Wadati, J. Phys. Soc.Japan.38, 673 (1975); ibid38,681 (1975). | ||
| + | * P.G. Kevrekidis, A. Khare, A. Saxena and G. Herring, J.Phys. A37, 10959 (2004). | ||
| + | * Z. Fu, S. Liu, S. Liu and Q. Zhao, Phys. Letts. A290,72 (2001). | ||
| + | |||
2015년 7월 9일 (목) 22:46 판
introduction
\[u_t+6uu_x+u_{xxx}=0\]
- mKdV equation
$$ u_t+6u^2u_x+u_{xxx}=0 $$
$N$-solution solution
- $N$-solution solution
$$ u(t,x)=-2\frac{\partial}{\partial x}\tan^{-1}[\frac{\Im \det (I+A)}{\Re \det (I+A)}] $$ where $I$ is the $N\times N$ matrix and $A$ denotes the $N\times N$ matrix with elements $$ A_{mn}=-\frac{d_n(t)}{\zeta_n+\zeta_m}\exp[i(\zeta_n+\zeta_m)x],\, m,n=1,2\cdots,N, $$ $\zeta_n=i\eta_n,\, \eta_n>0$ $d_n(t)=d_(0)\exp (8i\zeta_n^3 t)$
- see
- M. Wadati and K. Ohkuma, J. Phys. Soc. Japan. 51,2029 (1982).
- M. Wadati, J. Phys. Soc. Japan.77, 074005 (2008)
periodic solution
- M. Wadati, J. Phys. Soc. Japan.77, 074005 (2008)
- M. Wadati, J. Phys. Soc.Japan.38, 673 (1975); ibid38,681 (1975).
- P.G. Kevrekidis, A. Khare, A. Saxena and G. Herring, J.Phys. A37, 10959 (2004).
- Z. Fu, S. Liu, S. Liu and Q. Zhao, Phys. Letts. A290,72 (2001).
expositions
- Ho, C.-L., and P. Roy. ‘mKdV Equation Approach to Zero Energy States of Graphene’. arXiv:1507.02649 [cond-Mat, Physics:math-Ph, Physics:nlin, Physics:quant-Ph], 9 July 2015. http://arxiv.org/abs/1507.02649.
articles
- Germain, Pierre, Fabio Pusateri, and Frédéric Rousset. ‘Asymptotic Stability of Solitons for mKdV’. arXiv:1503.09143 [math], 31 March 2015. http://arxiv.org/abs/1503.09143.