Results 41 to 50 of about 1,801 (94)
Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$
Forum of Mathematics, PiWe 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 +2 more
doaj +1 more source
Set partitions and integrable hierarchies [PDF]
Theoretical and Mathematical Physics 2016, Volume 187, Issue 3, pp
842-870, 2015 We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
arxiv +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
Frobenius manifolds from regular classical $W$-algebras [PDF]
, 2010 We obtain polynomial Frobenius manifolds from classical $W$-algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.
arxiv +1 more source
Global well-posedness for KdV in Sobolev Spaces of negative index [PDF]
, 2001 The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data.
Colliander, J. +4 more
core +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 +12 more
core +1 more source
On the elliptic sinh-Gordon equation with Durham boundary conditions [PDF]
, 2020 We adapt Sklyanin's $K$-matrix formalism to the sinh-Gordon equation, and prove that all free boundary constant mean curvature (CMC) annuli in the unit ball in $\mathbb{R}^3$ are of finite type.
arxiv +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
Partial Differential Equations in Applied Mathematics, 2020 In this article, we apply a direct influential approach namely enhanced modified simple equation (EMSE) method to integrate the Burgers–Huxley (BH) and FitzHugh–Nagumo (FHN) equations which explain nerve pulse propagation in nerve fibers, circuit theory ...
Md. Mamunur Roshid +3 more
doaj
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 +2 more
core +1 more source