Long-time asymptotics for the Elastic Beam equation in the solitonless region via $\bar{\partial}$ methods
Analysis of PDEs
2023-09-08 v1 Exactly Solvable and Integrable Systems
Abstract
In this work, we study the Cauchy problem of the Elastic Beam equation with initial value in weighted Sobolev space via the -steepset descent method. Begin with the Lax pair of the Elastic Beam equation, we successfully derive the basic Riemann-Hilbert problem, which can be used to represent the solutions of the Elastic Beam equation. Then, considering the solitonless region and using the -steepset descent method, we analyse the long-time asymptotic behaviors of the solutions for the Elastic Beam equation.
Keywords
Cite
@article{arxiv.2309.03230,
title = {Long-time asymptotics for the Elastic Beam equation in the solitonless region via $\bar{\partial}$ methods},
author = {Wei-Qi Peng and Yong Chen},
journal= {arXiv preprint arXiv:2309.03230},
year = {2023}
}