Results 31 to 40 of about 929 (72)

Restricted Flows and the Soliton Equation with Self-Consistent Sources [PDF]

, 2006
The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Backlund transformation for the restricted flows (by V.B. Kuznetsov et al.
Lin, Runliang, Yao, Haishen, Zeng, Yunbo
core   +4 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

Evidence for the Nonintegrability of a Water Wave Equation in 2+1 Dimensions

, 2004
We provide evidence of the nonintegrability of a recently proposed model for water waves in 2+1 dimensions: we show that under a nonlinear time transformation, a certain reduction of this partial differential equation is mapped to an ordinary ...
P. R. Gordoa, A. Pickering, M. Senthilvelan   +2 more
semanticscholar   +1 more source

Non-commutative rational Yang-Baxter maps [PDF]

, 2013
Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising ...
Doliwa, Adam
core   +2 more sources

Rogue waves of the Fokas-Lenells equation

, 2012
The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schr\"odinger (NLS ...
He, Jingsong, Porsezian, Kuppuswamy, Xu, Shuwei   +2 more
core   +1 more source

Fractional Analogous Models in Mechanics and Gravity Theories [PDF]

, 2010
We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity and fractional
D Baleanu, D Baleanu, S Anco, S Vacaru, S Vacaru, S Vacaru   +5 more
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

Complete integrability versus symmetry

, 2012
The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of ...
Abraham R., Arnold V. I., Holm D. D., Holm D. D., Holm D. D., Kozlov V. V., Marsden J. E., Ratiu T. S., Răzvan M. Tudoran, Stephani H.   +9 more
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

On the non-integrability of the Popowicz peakon system [PDF]

, 2008
We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations.
Andrew N. W. Hone, Manuscript Submitted To, Michael V. Irle   +2 more
core   +3 more sources