"Modified KdV (mKdV) equation"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| + | ==introduction== | ||
| + | * [[KdV equation]] | ||
| + | :<math>u_t+6uu_x+u_{xxx}=0</math> | ||
| + | * mKdV equation | ||
| + | $$ | ||
| + | u_t+6u^2u_x+u_{xxx}=0 | ||
| + | $$ | ||
| + | * $N$-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 | ||
| + | $$ | ||
| + | A_{mn}=-\frac{d_n(t)}{\zeta_n+\zeta_m}\exp[i(\zeta_n+\zeta_m)x],\, m,n=1,2\cdots,N, | ||
| + | $$ | ||
| + | $\zeta_n=i\eta_n,\, \eta_n>0$ | ||
| + | $d_n(t)=d_(0)\exp (8i\zeta_n^3 t)$ | ||
| + | |||
| + | |||
| + | |||
==expositions== | ==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. | * 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. | ||
2015년 7월 9일 (목) 19:53 판
introduction
\[u_t+6uu_x+u_{xxx}=0\]
- mKdV equation
$$ u_t+6u^2u_x+u_{xxx}=0 $$
- $N$-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 $$ A_{mn}=-\frac{d_n(t)}{\zeta_n+\zeta_m}\exp[i(\zeta_n+\zeta_m)x],\, m,n=1,2\cdots,N, $$ $\zeta_n=i\eta_n,\, \eta_n>0$ $d_n(t)=d_(0)\exp (8i\zeta_n^3 t)$
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.