Modified KdV (mKdV) equation - 편집 역사

2020년 11월 16일 (월) 12:31에 Pythagoras0님의 편집

2020-11-16T12:31:31Z

2020-11-13T15:57:53Z

2016-05-06T01:27:59Z

section 'articles' updated

2015-07-10T07:17:42Z

$N$-solution solution

2015-07-10T07:09:16Z

$N$-solution solution

2015-07-10T06:46:30Z

2015-07-10T03:54:09Z

2015-07-10T03:53:25Z

2015-07-10T03:49:23Z

2015-07-10T03:42:31Z

@@ 3번째 줄: / 3번째 줄: @@
 :<math>u_t+6uu_x+u_{xxx}=0</math>
 * mKdV equation
-$$
+:<math>
 u_t+6u^2u_x+u_{xxx}=0
-$$
+</math>
-==$N$-solution solution==
+==<math>N</math>-solution solution==
-* $N$-solution solution
+* <math>N</math>-solution solution
-$$
+:<math>
 u(t,x)=-2\frac{\partial}{\partial x}\tan^{-1}[\frac{\Im \det (I+A)}{\Re \det (I+A)}]
-$$
+</math>
-where $I$ is the $N\times N$ matrix and $A$ denotes the $N\times N$ matrix with elements
+where <math>I</math> is the <math>N\times N</math> matrix and <math>A</math> denotes the <math>N\times N</math> matrix with elements
-$$
+:<math>
 A_{mn}=-\frac{d_n(t)}{\zeta_n+\zeta_m}\exp[i(\zeta_n+\zeta_m)x],\, m,n=1,2\cdots,N,
-$$
+</math>
-$\zeta_n=i\eta_n,\, \eta_n>0$
+<math>\zeta_n=i\eta_n,\, \eta_n>0</math>
-$d_n(t)=d_n(0)\exp (8i\zeta_n^3 t)$
+<math>d_n(t)=d_n(0)\exp (8i\zeta_n^3 t)</math>
-* 1-soliton, $\zeta=i\eta,\, \eta>0$
+* 1-soliton, <math>\zeta=i\eta,\, \eta>0</math>
-$$
+:<math>
 u(x)=-2\eta \operatorname{sech} (2\eta x)
-$$
+</math>
 * 2-soliton
 * see

← 이전 판		2020년 11월 13일 (금) 15:57 판
42번째 줄:		42번째 줄:
	* Miguel A. Alejo, Claudio Muñoz, José M. Palacios, On the variational structure of breather solutions, arXiv:1309.0625 [math-ph], September 03 2013, http://arxiv.org/abs/1309.0625		* Miguel A. Alejo, Claudio Muñoz, José M. Palacios, On the variational structure of breather solutions, arXiv:1309.0625 [math-ph], September 03 2013, http://arxiv.org/abs/1309.0625
	* 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.		* 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.
		+	[[분류:migrate]]

← 이전 판		2016년 5월 6일 (금) 01:27 판
40번째 줄:		40번째 줄:

	==articles==		==articles==
		+	* Miguel A. Alejo, Claudio Muñoz, José M. Palacios, On the variational structure of breather solutions, arXiv:1309.0625 [math-ph], September 03 2013, http://arxiv.org/abs/1309.0625
	* 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.		* 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.

@@ 20번째 줄: / 20번째 줄: @@
 * 1-soliton, $\zeta=i\eta,\, \eta>0$
 $$
-u(x)=-2\eta \sech (2\eta x)
+u(x)=-2\eta \operatorname{sech} (2\eta x)
 $$
 * 2-soliton

@@ 17번째 줄: / 17번째 줄: @@
 $$
 $\zeta_n=i\eta_n,\, \eta_n>0$
-$d_n(t)=d_(0)\exp (8i\zeta_n^3 t)$
+$d_n(t)=d_n(0)\exp (8i\zeta_n^3 t)$
 * see
 ** M. Wadati and K. Ohkuma, J. Phys. Soc. Japan. 51,2029 (1982).
 ** M. Wadati, J. Phys. Soc. Japan.77, 074005 (2008)
 ==periodic solution==

← 이전 판		2015년 7월 10일 (금) 03:53 판
1번째 줄:		1번째 줄:
		+	==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.

← 이전 판		2015년 7월 10일 (금) 03:49 판
1번째 줄:		1번째 줄:
		+	==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.
		+
		+
		+	==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.		* 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.

← 이전 판		2015년 7월 10일 (금) 03:42 판
1번째 줄:		1번째 줄:
		+	* 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.
	* 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.		* 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.