The initial-value problem for a Gardner-type equation
Year: 2025
Type: article
Abstract: Discussed here is a regularized version (0.1) u t + u x + u u x + A u 2 u x − u xxt = 0 , $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equation u t + u x + u u x + A u 2 u x + u xxx = 0 , $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx}}=0,$$ that arises in hydrodynamics and plasma physics. Considered here are well-posedness issues for the initial-value problem for the regularized equation posed on all of R $\mathbb{R}$ .
Source: Advanced Nonlinear Studies
Authors: Jerry Bona, Hongqiu Chen, Pamela Guerrero, Cristina Haidau, Sanja Pantic
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,469
OpenAlex ID: W4411021249