Results 31 to 40 of about 904 (79)

Unique continuation for discrete nonlinear wave equations [PDF]

, 2012
We establish unique continuation for various discrete nonlinear wave equations. For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some arbitrarily small time interval, then they coincide everywhere. Moreover,
Krueger, Helge, Teschl, Gerald
core   +3 more sources

Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation

Advances in Nonlinear Analysis
In this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the
Shan Minjie, Chen Mingjuan, Lu Yufeng, Wang Jing   +3 more
doaj   +1 more source

On the bi-Hamiltonian structure of Bogoyavlensky system on $so(4)$

, 2010
We discuss bi-Hamiltonian structure for the Bogoyavlensky system on $so(4)$ with an additional integral of fourth order in momenta. An explicit procedure to find the variables of separation and the separation relations is considered in ...
Vershilov, A. V.
core   +1 more source

Non-commutative q-Painleve VI equation [PDF]

, 2013
By applying suitable centrality condition to non-commutative non-isospectral lattice modified Gel'fand-Dikii type systems we obtain the corresponding non-autonomous equations. Then we derive non-commutative q-discrete Painleve VI equation with full range
Doliwa, Adam
core   +1 more source

Integrable 1D Toda cellular automata

, 2005
First, we recall the algebro-geometric method of construction of finite field valued solutions of the discrete KP equation and next we perform a reduction of the dKP equation to the discrete 1D Toda equation.
Bialecki, Mariusz
core   +2 more sources

Integrable system of null curve and Betchov-Da Rios equation

Demonstratio Mathematica
This study focuses on the time evolution of a null curve using a new frame and a new transformation in Minkowski 3-space. Accordingly, Landau–Lifshitz and coupled Boussinesq-like equations for the null curve are provided in terms of the new ...
Yoon Dae Won
doaj   +1 more source

Remarks on the waterbag model of dispersionless Toda Hierarchy

, 2007
We construct the free energy associated with the waterbag model of dToda.
Bogdanov L V, Boyarsky A, Boyer C P, Calderbank D M J, Chang J H, Dijkgraaf R, Dubrovin B, Dubrovin B, Jones P. E., Konopelchenko B. G., Kostov L, Krichever I., Krichever I., Marshakov A., Martinez Alonso L, Martini R., Mineev-Weinstein M., Pavlov M. V., Pavlov M. V., Riley A, Takasaki K., Takasaki K., Takasaki K., Takebe T, Tsarev S. P., Ward R. S., Wiegmann P., Wiegmann P., Witten E, Yu L.A.   +29 more
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B\"acklund-Darboux Transformations and Discretizations of Super KdV Equation [PDF]

, 2014
For a generalized super KdV equation, three Darboux transformations and the corresponding B\"acklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.
Liu, Qing Ping, Xue, Ling-Ling
core   +1 more source

Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
doaj   +1 more source

The Toda lattice is super-integrable

, 2005
We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom.
Adler, Atiyah, Christodoulos Sophocleous, Damianou, Damianou, Damianou, Faybusovich, Flaschka, Hénon, Manakov, Maria A. Agrotis, Pantelis A. Damianou, Toda   +12 more
core   +1 more source