Results 31 to 40 of about 863 (58)

The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients [PDF]

, 2006
The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable.
Kobayashi, Tadashi, Toda, Kouichi
core   +1 more source

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

Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras [PDF]

, 2006
The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to ...
Gerdjikov, Vladimir S., Grahovski, Georgi G.   +1 more
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

On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability [PDF]

, 2010
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm.
Golenia, Jolanta, Pavlov, Maxim V., Popowicz, Ziemowit, Prykarpatsky, Anatoliy K.   +3 more
core   +4 more sources

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

A Liouville theorem for the Degasperis-Procesi equation [PDF]

, 2015
We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution.
Brandolese, Lorenzo
core  

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

, 2013
In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element.
A. Alexandrov, A. Alexandrov, A. Alexandrov, A. Alexandrov, A. Alexandrov, A. Givental, A. Givental, A. Givental, A. Mironov, A. Mironov, A. Mironov, A. Morozov, A. Morozov, A. Okounkov, A.S. Alexandrov, A.S. Alexandrov, A.S. Alexandrov, A.S. Schwarz, Alexander Alexandrov, C. Faber, C. Itzykson, E. Witten, G. Borot, I. Goulden, I. Kostov, I. Kostov, I.P. Goulden, M. Aganagic, M. Kazarian, M. Kontsevich, S. Kharchev, T. Ekedahl, T. Miwa, T. Shiota, V. Bouchard, V. Kac   +35 more
core   +1 more source

Invertible Darboux Transformations [PDF]

, 2013
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae.
Shemyakova, Ekaterina
core   +3 more sources

The sixth Painleve equation arising from D_4^{(1)} hierarchy

, 2006
The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.Comment: 14 ...
Carter R, Delduc F, Iwasaki K, Kac V G, Kakei S Kikuchi T, Kawamuko H, Kenta Fuji, Noumi M, Noumi M, Noumi M Yamada Y Kirillov A N Tsuchiya A Umemura H, Takao Suzuki   +10 more
core   +1 more source