English

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 H1,1(R)H^{1,1}(\mathbb{R}) via the ˉ\bar{\partial}-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 ˉ\bar{\partial}-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}
}