Results 61 to 70 of about 1,133 (78)

Sharp local well-posedness for KP-I equations in the semilinear regime

Forum of Mathematics, Sigma
We show sharp well-posedness with analytic data-to-solution mapping in the semilinear regime for dispersion-generalized KP-I equations on $\mathbb {R}^2$ and $\mathbb {R} \times \mathbb {T}$ .
Shinya Kinoshita, Akansha Sanwal, Robert Schippa   +2 more
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

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

The AKNS-hierarchy [PDF]

, 2000
We present here an overview for the Encyclopaedia of Mathematics of the various forms and properties of this system of equations together with its geometric and Lie algebraic ...
Helminck, G.F.
core   +1 more source

Genus two KdV soliton gases and their long-time asymptotics

Forum of Mathematics, Sigma
This paper employs the Riemann-Hilbert problem and nonlinear steepest descent method of Deift-Zhou to provide a comprehensive analysis of the asymptotic behavior of the genus two Korteweg-de Vries soliton gases.
Deng-Shan Wang, Dinghao Zhu, Xiaodong Zhu   +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

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

Dissipative perturbations for the K(n,n) Rosenau-Hyman equation

, 2012
Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations.
Abassy, Antonova, Bertozzi, Bin, Biswas, Biswas, Biswas, Cardenas, Cooper, Cooper, Cooper, de Frutos, Dey, Drazin, Ebadi, Fernandez, Francisco R. Villatoro, Johnson, Julio Garralón, Kardashov, Kevorkian, Khare, Kivshar, Kivshar, Kovalev, Laila, Lamb, Ludu, McLaughlin, Mihaila, Olver, Pikovsky, Rosenau, Rosenau, Rosenau, Rosenau, Rosenau, Rosenau, Rus, Rus, Rus, Rus, Triki, Zhang   +43 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