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	~~The '''Ishimori equation (IE)'''~~ is a ~~[[partial differential equation]] proposed by~~ the ~~Japanese [[mathematician]] {{harvtxt\|Yuji Ishimori\|1984}}~~. ~~Its interest~~ is as the ~~first example~~ of ~~a nonlinear spin-one field model in the plane that is [[integrable system\|integrable]] {{harv\|Sattinger\|Tracy\|Venakides\|1991\|p=78}}~~.		Cydia is a software utility that permits you to set up new applications and games in your Apple iPhone. Though there are literally thousands of apps accessible in the Apple iStore, some Cydia are lots higher than the ones accessible there. WinterBoard is one such app that allows you to modify and customise the entire feel and appear of your iPhone.<br><br>So why should you pay any money for a online game when you can get Dungeon Hunter four Hack and enjoyment of all of the options the online game the right manner. Get all of the gold, gems to have the ability to unlock every product you really need within the online game, speed up your digital blacksmith, and so forth with out spending a single dime out of your wallet. Dungeon Hunter 4 Hack will only price you a few minutes of your time to complete a quick survey to open the declare obtain. This is required in order to support our website and to have the ability to deliver you extra exceptional things in the future<br><br>Dungeon Hunter 4 Hack Instrument No Survey Download Dungeon Hunter 4 Hack Tool Dungeon Hunter four Hack No Jailbreak Hack Dungeon Hunter 4 With out Jailbreak Dungeon Hunter four hack no jailbreak Dungeon Hunter four Cydia Hack Dungeon Hunter 4 hack app Dungeon Hunter four cydia hack Dungeon Hunter four Power Hack Dungeon Hunter 4 hack obtain no survey Dragon Hunter four hack Dungeon Hunter 4 Hack Gems And Gold dungeon hunter four hack device android without survey Dungeon Hunter 4 Hack Features Dungeon Hunter 4 iphone hack free Dungeon Hunter 4 Hack APK Dungeon Hunter 4 hack ipod dungeon hunter four hack gratuit Start the Dungeon Hunter 4 Hack Tool. Hack for unlimited Gems Dungeon Hunter outil 4 hack Hack for limitless Gold dungeon hunter four hack cheats tool gratuit Dungeon Hunter four hack mac dungeon hunter four hack ipa Add Limitless Gems Hack<br><br>Connectez votre [http://appareilios.com/ appareil iOS] ou Android à l'ordinateur via USB. (Dungeon Hunter four doit être installé et fonctionner avec une connexion Web.) Every day updates to make sure the performance of the hacking software. However that is not enough. On September 26, 2013, Glu Video games quietly tender-launched Eternity Warriors three in the New Zealand App Retailer. It is one more spectacularly rendered effort that makes an attempt to blow its followers away with two extra characters (Mage and Monk), incredibly gorgeous visuals and in-sport real-time chat. LOOT numerous objects Select from four varieties of warriors with unique combat types Bear in mind the sole function of the leaked letter to publishers and builders is for creating open traces of communication. Modern Fight 3 IDA Best Cydia Apps Finest Cydia Sources<br><br>If you have any thoughts with regards to exactly where and how to use [http://www.acabottutor.com/130039 Dungeon Hunter 4 Cheats], you can get hold of us at our internet site.

	~~==Equation==~~
	~~The Ishimori Equation has the form~~

	:<~~math~~> \frac{\partial \mathbf{S}}{\partial t} = \mathbf{S}\wedge \left(\frac{\partial^2 \mathbf{S}}{\partial x^{2}} + \frac{\partial^2 \mathbf{S}}{\partial y^{2}}\right)+ \frac{\partial u}{\partial x}\frac{\partial \mathbf{S}}{\partial y} + \frac{\partial u}{\partial y}\frac{\partial \mathbf{S}}{\partial x},\qquad (1a)<~~/math~~>

	:<math> \frac{\partial^2 u}{\partial x^2}-\alpha^2 \frac{\partial^2 u}{\partial y^2}=-2\alpha^2 \mathbf{S}\cdot\left(\frac{\partial \mathbf{S}}{\partial x}\wedge \frac{\partial \mathbf{S}}{\partial y}\right).~~\qquad (1b)</math>~~

	~~==Lax representation==~~

	~~The [[Lax representation]]~~

	~~:<math>L_t=AL-LA\qquad (2)</math>~~

	of the ~~equation is given by~~

	~~:<math>L=\Sigma \partial_x+\alpha I\partial_y~~,~~\qquad (3a)</math>~~

	~~:<math>A= -2i\Sigma\partial_x^2+(-i\Sigma_x-i\alpha\Sigma_y\Sigma+u_yI-\alpha^3u_x\Sigma)\partial_x~~.~~\qquad (3b)~~<~~/math~~>

	~~Here~~

	:<~~math~~>~~\Sigma=\sum_{j=1}^3S_j\sigma_j,\qquad (~~4~~)</math>~~

	the <~~math~~>~~\sigma_i~~<~~/math~~> ~~are the~~ [~~[Pauli matrices]] and <math>I<~~/~~math> is the identity matrix~~.

	~~==Reductions==~~
	~~IE admits an important reduction:~~
	~~in 1+1 dimensions it reduces to the [[Heisenberg model (classical)\|continuous classical Heisenberg ferromagnet equation]~~] (~~CCHFE~~)~~. The CCHFE is integrable.~~

	~~==Equivalent counterpart==~~
	~~The equivalent counterpart~~ of the IE is ~~the [[Davey-Stewartson equation]]~~.

	~~==See also==~~

	* [[Nonlinear Schrödinger equation]]
	* [[Heisenberg model (classical)]]
	* [[Spin wave]]
	* [[Landau-~~Lifshitz equation]]~~
	* [[Soliton]]
	* [[Vortex]]
	* [[Nonlinear systems]]
	* [[Davey–Stewartson equation]]

	~~==References==~~
	* {{citation\|last=Gutshabash \|first=E.Sh. \|title=Generalized Darboux transform in the ~~Ishimori magnet model on the background of spiral structures\|journal=JETP Letters\|volume=78\|issue=11\|pages=740–744 \|year=2003\|doi=10~~.~~1134/1.1648299}}~~
	*{{citation\|last=Ishimori\|first=Yuji\|title=Multi-vortex solutions of a two~~-dimensional nonlinear wave equation\|journal=Prog. Theor. Phys. \|volume=72\|year=1984\|pages=33–37~~
	~~\|doi= 10.1143/PTP.72.33\|mr=0760959}}~~
	*{{citation\|last=Konopelchenko \|first=B.G. \|title=Solitons in ~~multidimensions\|publisher= World Scientific \|year=1993\|isbn=978-981-02~~-~~1348~~-~~0}}~~
	*{{citation\|last= Martina\|first= L.~~\|last2= Profilo \|first2=G.\|last3= Soliani\|first3= G.\|last4= Solombrino \|first4=L. \|title=Nonlinear excitations~~ in ~~a Hamiltonian spin-field model in 2+1 dimensions \|journal=Phys. Rev. B \|volume=49\|pages=12915–12922 \|year=1994\|doi= 10.1103/PhysRevB.49.12915\|issue= 18}}~~
	*{{citation\|editor1-first=David H.\|editor1-last= Sattinger\|editor2-first= C. A. \|editor2-last=Tracy \|title=Inverse Scattering and ~~Applications\|year= 1991~~
	~~\|editor3-first=S.\|editor3-last= Venakides\|series= Contemporary Mathematics\|volume= 122\|publisher= American Mathematical Society\|place= Providence, RI\|isbn=0-8218-5129-2\|mr=1135850 }}~~
	*{{citation\|first=Li-yeng \|last=Sung\|title= The Cauchy problem for ~~the Ishimori equation\|journal= Journal~~ of ~~Functional Analysis\|volume=139\|pages=29–67 \|year=1996\|doi=10~~.~~1006/jfan.1996.0078}}~~
	~~==External links==~~
	*[http://~~tosio~~.~~math~~.~~toronto.edu~~/~~wiki/index.php/Ishimori_system Ishimori_system~~] at ~~the dispersive equations wiki~~

	~~[[Category:Electric and magnetic fields in matter]]~~
	~~[[Category:Partial differential equations]]~~

en>069952497a: Reverted edit(s) by 81.147.118.219 identified as test/vandalism using STiki

2013-07-12T12:35:13Z

Reverted edit(s) by 81.147.118.219 identified as test/vandalism using STiki

← Older revision		Revision as of 14:35, 12 July 2013
Line 1:		Line 1:
	~~59 yrs old Futures Trader Ernie Engebretson from Cranbrook~~, ~~spends time with pursuits like web~~, ~~Dungeon Hunter~~ 4 ~~Hack~~ and ~~history~~. ~~Remembers what a remarkable spot~~ it ~~was having gone~~ to ~~Historic Centre~~ of ~~Évora~~.~~<br><br>my web site;~~ [http://~~www~~.~~acabottutor~~.~~com~~/~~130039 Dungeon Hunter 4 Cheats~~]		The '''Ishimori equation (IE)''' is a [[partial differential equation]] proposed by the Japanese [[mathematician]] {{harvtxt\|Yuji Ishimori\|1984}}. Its interest is as the first example of a nonlinear spin-one field model in the plane that is [[integrable system\|integrable]] {{harv\|Sattinger\|Tracy\|Venakides\|1991\|p=78}}.

			==Equation==
			The Ishimori Equation has the form

			:<math> \frac{\partial \mathbf{S}}{\partial t} = \mathbf{S}\wedge \left(\frac{\partial^2 \mathbf{S}}{\partial x^{2}} + \frac{\partial^2 \mathbf{S}}{\partial y^{2}}\right)+ \frac{\partial u}{\partial x}\frac{\partial \mathbf{S}}{\partial y} + \frac{\partial u}{\partial y}\frac{\partial \mathbf{S}}{\partial x},\qquad (1a)</math>

			:<math> \frac{\partial^2 u}{\partial x^2}-\alpha^2 \frac{\partial^2 u}{\partial y^2}=-2\alpha^2 \mathbf{S}\cdot\left(\frac{\partial \mathbf{S}}{\partial x}\wedge \frac{\partial \mathbf{S}}{\partial y}\right).\qquad (1b)</math>

			==Lax representation==

			The [[Lax representation]]

			:<math>L_t=AL-LA\qquad (2)</math>

			of the equation is given by

			:<math>L=\Sigma \partial_x+\alpha I\partial_y,\qquad (3a)</math>

			:<math>A= -2i\Sigma\partial_x^2+(-i\Sigma_x-i\alpha\Sigma_y\Sigma+u_yI-\alpha^3u_x\Sigma)\partial_x.\qquad (3b)</math>

			Here

			:<math>\Sigma=\sum_{j=1}^3S_j\sigma_j,\qquad (4)</math>

			the <math>\sigma_i</math> are the [[Pauli matrices]] and <math>I</math> is the identity matrix.

			==Reductions==
			IE admits an important reduction:
			in 1+1 dimensions it reduces to the [[Heisenberg model (classical)\|continuous classical Heisenberg ferromagnet equation]] (CCHFE). The CCHFE is integrable.

			==Equivalent counterpart==
			The equivalent counterpart of the IE is the [[Davey-Stewartson equation]].

			==See also==

			* [[Nonlinear Schrödinger equation]]
			* [[Heisenberg model (classical)]]
			* [[Spin wave]]
			* [[Landau-Lifshitz equation]]
			* [[Soliton]]
			* [[Vortex]]
			* [[Nonlinear systems]]
			* [[Davey–Stewartson equation]]

			==References==
			* {{citation\|last=Gutshabash \|first=E.Sh. \|title=Generalized Darboux transform in the Ishimori magnet model on the background of spiral structures\|journal=JETP Letters\|volume=78\|issue=11\|pages=740–744 \|year=2003\|doi=10.1134/1.1648299}}
			*{{citation\|last=Ishimori\|first=Yuji\|title=Multi-vortex solutions of a two-dimensional nonlinear wave equation\|journal=Prog. Theor. Phys. \|volume=72\|year=1984\|pages=33–37
			\|doi= 10.1143/PTP.72.33\|mr=0760959}}
			*{{citation\|last=Konopelchenko \|first=B.G. \|title=Solitons in multidimensions\|publisher= World Scientific \|year=1993\|isbn=978-981-02-1348-0}}
			*{{citation\|last= Martina\|first= L.\|last2= Profilo \|first2=G.\|last3= Soliani\|first3= G.\|last4= Solombrino \|first4=L. \|title=Nonlinear excitations in a Hamiltonian spin-field model in 2+1 dimensions \|journal=Phys. Rev. B \|volume=49\|pages=12915–12922 \|year=1994\|doi= 10.1103/PhysRevB.49.12915\|issue= 18}}
			*{{citation\|editor1-first=David H.\|editor1-last= Sattinger\|editor2-first= C. A. \|editor2-last=Tracy \|title=Inverse Scattering and Applications\|year= 1991
			\|editor3-first=S.\|editor3-last= Venakides\|series= Contemporary Mathematics\|volume= 122\|publisher= American Mathematical Society\|place= Providence, RI\|isbn=0-8218-5129-2\|mr=1135850 }}
			*{{citation\|first=Li-yeng \|last=Sung\|title= The Cauchy problem for the Ishimori equation\|journal= Journal of Functional Analysis\|volume=139\|pages=29–67 \|year=1996\|doi=10.1006/jfan.1996.0078}}
			==External links==
			*[http://tosio.math.toronto.edu/wiki/index.php/Ishimori_system Ishimori_system] at the dispersive equations wiki

			[[Category:Electric and magnetic fields in matter]]
			[[Category:Partial differential equations]]

192.167.204.14: /* References */ - broken links, +link to chemwiki

2012-07-12T07:50:21Z

References: - broken links, +link to chemwiki

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59 yrs old Futures Trader Ernie Engebretson from Cranbrook, spends time with pursuits like web, Dungeon Hunter 4 Hack and history. Remembers what a remarkable spot it was having gone to Historic Centre of Évora.<br><br>my web site; [http://www.acabottutor.com/130039 Dungeon Hunter 4 Cheats]