Academic Journal
Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity
| Title: | Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity |
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| 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 |
| ISSN: | 17760852 |
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| DOI: | 10.1007/s44198-023-00131-7 |