Results 61 to 70 of about 1,801 (94)
Parametrized vector fields and the zero-curvature condition [PDF]
arXiv, 2004 We apply the notion of parametrized vector field on a manifold M, where the parameters are also in M, to the study of the zero-curvature condition that arises in the context of integrable systems.
arxiv
Results in Physics, 2016 The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation.
Chen Yue, Aly Seadawy, Dianchen Lu
doaj
On a unified formulation of completely integrable systems
, 2011 The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $\Omega\subseteq \R^n$, is essentially $\mathcal{C}^1 ...
Abraham +14 more
core +1 more source
Reciprocal transformations and deformations of integrable hierarchies [PDF]
arXiv, 2008 We present changes of variables that transform new integrable hierarchies found by Szablikowski and B{\l}aszak using the $R$-matrix deformation technique [J. Math. Phys. 47 (2006), paper 043505, nlin.SI/0501044] into known Harry-Dym-type and mKdV-type hierarchies.
arxiv
Exact solution of generalized inviscid Burgers' equation [PDF]
arXiv, 2009 Let $f,g:{\Bbb R}\to{\Bbb R}$ be integrable functions, $f$ nowhere zero, and $\phi (u)=\int du/f(u)$ be invertible. An exact solution to the generalized nonhomogeneous inviscid Burgers' equation $u_t+g(u).u_x=f(u)$ is given, by quadratures.
arxiv
Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables [PDF]
arXiv, 2009 We consider the KdV equation on the Sobolev space of periodic distributions. We obtain estimates of the solution of the KdV in terms of action variables.
arxiv
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 +35 more
core +1 more source
Arnold-Liouville theorem for integrable PDEs: a case study of the focusing NLS equation [PDF]
arXiv, 2020 We prove an infinite dimensional version of the Arnold-Liouville theorem for integrable non-linear PDEs: In a case study we consider the {\em focusing} NLS equation with periodic boundary conditions.
arxiv
A 3-component extension of the Camassa-Holm hierarchy
, 2006 We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a 3-component extension of ...
B. Fuchssteiner +22 more
core +1 more source
Reciprocal link among the Qiao-Liu peakon equation and the modified Korteweg-de Vries equation [PDF]
arXiv, 2010 This paper has been withdrawn by the author. The result is already known.
arxiv