Results 11 to 20 of about 91 (52)

Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions

Forum of Mathematics, Sigma
We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity.
Mihaela Ifrim, Annalaura Stingo
doaj   +1 more source

Investigating traveling wave structures in the van der Waals normal form for fluidized granular matter through the modified S-expansion method

Partial Differential Equations in Applied Mathematics
This research discovers traveling wave solutions (TWSs) of the van der Waals normal form for fluidized granular matter using the modified S-expansion (MS-E) method.
Hamida Parvin, Md. Nur Alam, Md. Abdullah Bin Masud, Md. Jakir Hossen   +3 more
doaj   +1 more source

Random data Cauchy theory for supercritical wave equations II : A global existence result

, 2007
We prove that the subquartic wave equation on the three dimensional ball $\Theta$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_ ...
J. Bourgain, J. Bourgain, J. Szeftel, J.L. Lions, N. Burq, N. Tzvetkov, Nicolas Burq, Nikolay Tzvetkov, P. Zhidkov, S. Kuksin   +9 more
core   +2 more sources

Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience

Partial Differential Equations in Applied Mathematics
Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering ...
Md. Nur Alam, Md. Azizur Rahman
doaj   +1 more source

Energy scattering for 2D critical wave equation

, 2008
We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the
Ibrahim, Slim, Majdoub, Mohamed, Masmoudi, Nader, Nakanishi, Kenji   +3 more
core   +1 more source

On well-posedness of energy supercritical NLS on product space Rn×T4−n ${\mathbb{R}}^{n}{\times}{\mathbb{T}}^{4-n}$ (n = 0, 1, 2, 3)

Advances in Nonlinear Analysis
We establish the well-posedness theory for the quintic nonlinear Schrödinger equation (NLS) on four-dimensional tori (i.e., T4 ${\mathbb{T}}^{4}$ ), which is an energy-supercritical model. Compared to the recent breakthrough work (B. Kwak and S.
Wang Han, Li Xing, Lyu Ziyue, Zhao Zehua, Zhou Wenyu   +4 more
doaj   +1 more source

Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense

Partial Differential Equations in Applied Mathematics
This study examines how Stratonovich integrals (SIs) affect the solutions of the Heisenberg ferromagnetic spin chain (HFSC) equation using the modified (G'/G)-expansion (MG'/GE) scheme.
Md. Nur Alam
doaj   +1 more source

Nonlinear Waves and Dispersive Equations [PDF]

, 2013
Nonlinear dispersive equations are models for nonlinear waves in a wide range of physical contexts. Mathematically they display an interplay between linear dispersion and nonlinear interactions, which can result in a wide range of outcomes from finite ...

core   +2 more sources

Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3

, 2013
Consider a bilinear interaction between two linear dispersive waves with a generic resonant structure (roughly speaking, space and time resonant sets intersect transversally).
Bernicot, Frederic, Germain, Pierre
core   +1 more source

Almost sure well-posedness of the cubic nonlinear Schr\"odinger equation below L^2(T) [PDF]

, 2011
We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear Schr\"odinger equation (NLS) with initial data below L^2. In particular, we exhibit nonlinear smoothing when the initial data are randomized.
Colliander, James, Oh, Tadahiro
core   +2 more sources