The intermediate nonlinear Schrodinger equation is locally well-posed in H^s for all s>0, and its integrable cases are globally well-posed for small L2 data when 0<s<1/2.
Global well-posedness for intermediate NLS with nonvanishing conditions at infinity
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The intermediate nonlinear Schr\"odinger equation (INLS) describes the dynamics of the envelope of weakly nonlinear internal waves in a stratified fluid of finite depth. While the INLS equation is known to admit dark soliton solutions, these solutions possess nonvanishing boundary conditions at spatial infinity and therefore fall outside the scope of existing well-posedness frameworks. This paper establishes the local and global well-posedness of a generalized INLS equation in Zhidkov-type spaces tailored to these nonvanishing boundary conditions. Furthermore, we rigorously justify the deep-water limit, proving that solutions of the generalized INLS converge to those of the generalized Calogero-Moser (CM) derivative NLS equation in Zhidkov-type spaces. Our well-posedness theory relies on the modified energy method combined with frequency envelopes, marking the first application of these techniques to Zhidkov-type spaces.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Sub-critical well-posedness for the intermediate nonlinear Schr\"{o}dinger equation on the line
The intermediate nonlinear Schrodinger equation is locally well-posed in H^s for all s>0, and its integrable cases are globally well-posed for small L2 data when 0<s<1/2.