Stability analysis for planar traveling solutions for nonlinear dispersive equations

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K05332
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Hiroshima University
• Principal Investigator: Mizumachi Tetsu 広島大学, 先進理工系科学研究科(理), 教授 (60315827)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: Benney Luke 方程式 / 線状孤立波解 / 安定性 / 長波長近似モデル / KP-II方程式

Outline of Final Research Achievements

I prove transverse stability of line solitary wave solutions for the Benney-Luke equations which is a long wave model for 3-dimensional water waves. The Benney-Luke is an isotropic model whereas the KP-II equation is a unidirectional model. Nevertheless, it turns out that perturbations to a line solitary wave propagate along its crest in the same manner as those for the KP-II equation. I also prove that phase shift of modulating line solitary waves for the KP-II equation and the Benney-Luke equation remains small for all the time.

Free Research Field

非線形偏微分方程式

Academic Significance and Societal Importance of the Research Achievements

３次元水面波の長波長近似モデルの線状孤立波解の全空間における安定性は，完全可積分系の方程式であるKP-II方程式の場合に知られていたが，完全可積分系でないBenney-Luke方程式に対しても同様の結果を得ることが出来た．