Rogue wave solution for nonlinear evolution equations and its algebraic structure

2017 Fiscal Year Final Research Report

• Project/Area Number: 26610029
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Kobe University
• Principal Investigator: Ohta Yasuhiro 神戸大学, 理学研究科, 教授 (10213745)
• Co-Investigator(Kenkyū-buntansha): 山田 泰彦 神戸大学, 理学研究科, 教授 (00202383) ; 野海 正俊 神戸大学, 理学研究科, 教授 (80164672)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 関数方程式論 / 応用数学

Outline of Final Research Achievements

Rogue wave is a class of solutions for some nonlinear evolution equations which are localized both in time and space. These solutions have rich mathematical structures and describe some interesting phenomena in various physical systems. The theory of integrable systems is applied to investigate the rogue wave solutions for some nonlinear evolution equations. A method to construct general rogue wave solutions is proposed and based on the determinant representation of rogue wave solutions, the algebraic structure of the space of solutions is studied.

Free Research Field

応用数学