Asian Journal of Mathematics and Computer Research

Small Data Scattering for the Global Solutions of the Supercritical Generalized KdV Equation

Xiaoya Tang *

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR, China.

Shanshan Zheng

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR, China.

*Author to whom correspondence should be addressed.

---

Abstract

We consider the scattering problem for the global solutions of the supercritical generalized KdV equation ∂_tu+∂_xxxu+μ∂_x(u^k+1) = 0, where k > 4 is an integer, initial data u₀ belongs to H¹(ℝ), and μ = ±1. To solve the scattering problem, a scattering criteria is established firstly, and then a new inequality is introduced to obtain uniformly bounded solutions in H¹(ℝ). Finally, we further clarify the conditions for the equation to have a global solution scattering in H¹(ℝ). Our method is mainly inspired by the works of Farah, Linares, Pastor, and Visciglia.

Keywords: Supercritical, generalized KdV equation, scattering, global solution

---

---