Eigenfunctions and Very Singular Similarity Solutions of Odd-Order Nonlinear Dispersion PDEs
R. S. Fernandes, V. A. Galaktionov
TL;DR
This paper investigates the asymptotic behavior of solutions to odd-order nonlinear dispersion PDEs, constructing global similarity solutions that correspond to eigenfunctions of associated rescaled ordinary differential equations.
Contribution
It introduces a method to construct global similarity solutions for odd-order nonlinear dispersion equations via eigenfunctions of rescaled ODEs, advancing understanding of their asymptotic properties.
Findings
Construction of global similarity solutions
Identification of eigenfunctions of rescaled ODEs
Insights into asymptotic solution behavior
Abstract
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Nonlinear Photonic Systems