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(uk+1) = 0, where k > 4 is an integer, initial data u0 belongs to H1(), 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(). Finally, we further clarify the conditions for the equation to have a global solution scattering in H1(). Our method is mainly inspired by the works of Farah, Linares, Pastor, and Visciglia.

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


How to Cite

Tang, X., & Zheng, S. (2024). Small Data Scattering for the Global Solutions of the Supercritical Generalized KdV Equation. Asian Journal of Mathematics and Computer Research, 31(1), 26–41. https://doi.org/10.56557/ajomcor/2024/v31i18519

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