Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity

Bibliographic Details
Title: Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity
Authors: Beatriz Juarez‐Campos, José de Jesús Villela‐Aguilar, Rafael Carreño‐Bolaños
Source: Journal of Nonlinear Mathematical Physics. 30:1316-1326
Publisher Information: Springer Science and Business Media LLC, 2023.
Publication Year: 2023
Subject Terms: Computer Networks and Communications, Energy-Critical Equations, Statistical and Nonlinear Physics, 16. Peace & justice, Korteweg-de Vries Equation, Computer science, 01 natural sciences, Dispersive Equations, Algorithm, Physics and Astronomy, Dynamics of Synchronization in Complex Networks, Nonlinear Dynamics, Discrete Solitons in Nonlinear Photonic Systems, Physical Sciences, Computer Science, 0103 physical sciences, FOS: Mathematics, Nonlinear Schrödinger Equation, Global Well-Posedness of Nonlinear Wave Equations, 0101 mathematics, Mathematical Physics, Mathematics
Description: We study the periodic problem for the Korteweg–de Vries equation with Landau damping, linear pumping and a higher-order convective nonlinearity $$\begin{aligned} \left\{ \begin{array}{c} w_{t}+w_{xxx}-\alpha w_{xx}=\beta w+\lambda w_{x}^{2}w_{xx},\text { }x\in \Omega ,t>0,\\ w(0,x)=\psi \left( x\right) ,\text { }x\in \Omega , \end{array} \right. \end{aligned}$$ w t + w xxx - α w xx = β w + λ w x 2 w xx , x ∈ Ω , t > 0 , w ( 0 , x ) = ψ x , x ∈ Ω , where, $$\alpha ,\beta >0,$$ α , β > 0 , $$\lambda \in \mathbb {R},$$ λ ∈ R , $$\Omega =\left[ -\pi ,\pi \right] .$$ Ω = - π , π . We assume that the initial data $$\psi \left( x\right) $$ ψ x are $$2\pi $$ 2 π - periodic. We prove the global existence of solutions and analyze their large-time asymptotics.
Document Type: Article
Other literature type
Language: English
ISSN: 1776-0852
DOI: 10.1007/s44198-023-00131-7
DOI: 10.60692/qcra9-ksv89
DOI: 10.60692/a10vx-64247
Rights: CC BY
Accession Number: edsair.doi.dedup.....c0f3648b7d6559a8567d404ccdca1c1f
Database: OpenAIRE
Description
ISSN:17760852
DOI:10.1007/s44198-023-00131-7