Results 61 to 70 of about 1,131 (79)

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

Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

Advances in Nonlinear Analysis, 2017
In this paper, we study the following water wave model with a nonlocal viscous term:
Goubet Olivier, Manoubi Imen
doaj   +1 more source

Wave breaking of periodic solutions to the Fornberg-Whitham equation

, 2017
Based on recent well-posedness results in Sobolev (or Besov spaces) for periodic solutions to the Fornberg-Whitham equations we investigate here the questions of wave breaking and blow-up for these solutions.
Hoermann, Guenther
core   +1 more source

Soliton solution of the osmosis K(2, 2) equation

, 2009
In this Letter, by using the bifurcation method of dynamical systems, we obtain the analytic expressions of soliton solution of the osmosis K(2, 2) equation.Comment: 8 ...
Biswas, Jiangbo Zhou, Lixin Tian, Luo, Rosenau, Wazwaz, Wazwaz, Wazwaz, Xu, Yan, Zhu   +10 more
core   +1 more source

On the existence of bound and ground states for some coupled nonlinear Schrödinger–Korteweg–de Vries equations

Advances in Nonlinear Analysis, 2017
We show the existence of positive bound and ground states for a system of coupled nonlinear Schrödinger–Korteweg–de Vries equations. More precisely, we prove that there exists a positive radially symmetric ground state if either the coupling coefficient ...
Colorado Eduardo
doaj   +1 more source

A remark on Gibbs measures with log-correlated Gaussian fields

Forum of Mathematics, Sigma
We study Gibbs measures with log-correlated base Gaussian fields on the d-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson’s argument.
Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo   +2 more
doaj   +1 more source

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, B. Khesin, E.G. Reyes, G. Falqui, H. McKean, J.E. Marsden, L.A. Dickey, Laura Fontanelli, M. Pedroni, Marco Pedroni, P. Casati, P. Casati, P. Casati, P. Libermann, P. Lorenzoni, Paolo Lorenzoni, R. Beals, R. Beals, R. Camassa, S. Abenda, S. Liu, V.E. Zakharov, V.G. Drinfeld   +22 more
core   +1 more source

Variational derivation of two-component Camassa-Holm shallow water system

, 2012
By a variational approach in the Lagrangian formalism, we derive the nonlinear integrable two-component Camassa-Holm system (1). We show that the two-component Camassa-Holm system (1) with the plus sign arises as an approximation to the Euler equations ...
Abraham R, Benney DJ, Constantin A, Delia Ionescu-Kruse, Holm DD, Lighthill J, Manin YuI   +6 more
core   +1 more source

R-matrix for a geodesic flow associated with a new integrable peakon equation

, 2016
We use the r-matrix formulation to show the integrability of geodesic flow on an $N$-dimensional space with coordinates $q_k$, with $k=1,...,N$, equipped with the co-metric $g^{ij}=e^{-|q_i-q_j|}\big(2-e^{-|q_i-q_j|}\big)$.
Holm, Darryl D., Qiao, Zhijun
core  

On generating functions in additive number theory, II: lower-order terms and applications to PDEs. [PDF]

Math Ann, 2021
Brandes J, Parsell ST, Poulias C, Shakan G, Vaughan RC.   +4 more
europepmc   +1 more source