Long-time asymptotics of the Sawada-Kotera equation and Kaup-Kupershmidt equation on the line

2023/07/17 by Deng‐Shan Wang, Xiaodong Zhu, Wang, Deng-Shan +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2307.08196

openalex publication_date 2023/07/17 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28

Abstract

Both Sawada-Kotera (SK) equation and Kaup-Kupershmidt (KK) equation are integrable systems with third-order Lax operator. Moreover, they are related with the same modified nonlinear equation (called modified SK-KK equation) by Miura transformations. This work first constructs the Riemann-Hilbert problem associated with the SK equation, KK equation and modified SK-KK equation by direct and inverse scattering transforms. Then the long-time asymptotics of these equations are studied based on Deift-Zhou steepest-descent method for Riemann-Hilbert problem. Finally, it is shown that the asymptotic solutions match very well with the results of direct numerical simulations.

Related

• Long-time asymptotics of the Sawada-Kotera equation on the line
• Nonlinear Fourier Transforms for the Sawada–Kotera Equation on the Line
• Long-time asymptotics for the short pulse equation
• Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data
• Soliton solutions to the Sawada--Kotera equation