Nonlinear Systems and Their Remarkable Mathematical Structures

Volume 3, Contributions from China

Norbert Euler, Da-jun Zhang, Norbert Euler, Da-jun Zhang

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Print ISBN: 9780367541088
• eBook ISBN: 9781000423303
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists).

Features

• Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area .
• Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering Sciences.
• Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained.

B7. Two hierarchies of multiple solitons and soliton molecules of (2+1)-dimensional Sawada-Kotera type equations

Ruoxia Yao ^a, Wei Wang^a,b and Yan Li ^a

^a School of Computer Science, Shaanxi Normal University, Xi'an, 710119, P.R.China

^b Information and Education Technology Center, Xi'an University of Finance and Economics, Xi'an, 710062, P.R.China

Abstract

Two transformations $v=p{(\text{ln}f)}_{xx}(p=2,4)$ that produce a trilinear and a quintic linear equation solved by two pairs of Hirota's bilinear equations respectively and the corresponding bilinearizations of a (2+1)-dimensional Sawada-Kotera (2DSK) type equation are reported. The two pairs of Hirota's bilinear equations, one is the normal (2+1)-dimensional bilinear SK equation and the other is a variant bilinear Kadomtsev-Petviashvili (KP) equation, are both obtained from the SK and variant KP (vKP) equations by $v=2{(\text{ln}f)}_{xx}$. Two hierarchies of multiple solitons and soliton molecule...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• The Authors
• A1. The BKP hierarchy and the modified BKP hierarchy
• A2. Elementary introduction to the direct linearisation of integrable systems
• A3. Discrete Boussinesq-type equations
• A4. The study of integrable hierarchies in terms of Liouville correspondences
• A5. Darboux transformations for supersymmetric integrable systems: A brief review
• A6. Nonlocal symmetries of nonlinear integrable systems
• A7. High-order soliton matrix for an extended nonlinear Schrödinger equation
• A8. Darboux transformation for integrable systems with symmetries
• A9. Frobenius manifolds and Orbit spaces of reflection groups and their extensions
• B1. On finite Toda type lattices and multipeakons of the Camassa-Holm type equations
• B2. Long-time asymptotics for the generalized coupled derivative nonlinear Schrödinger equation
• B3. Bilinearization of nonlinear integrable evolution equations: Recursion operator approach
• B4. Rogue wave patterns and modulational instability in nonlinear Schrödinger hierarchy
• B5. Algebro-geometric solutions to the modified Blaszak-Marciniak lattice hierarchy
• B6. Long-time asymptotic behavior of the modified Schrödinger equation via ∂¯-steepest descent method
• B7. Two hierarchies of multiple solitons and soliton molecules of (2+1)-dimensional Sawada-Kotera type equation
• B8. Dressing the boundary: exact solutions of soliton equations on the half-line
• B9. From integrable spatial discrete hierarchy to integrable nonlinear PDE hierarchy