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
• ISBN:
  9781000423303
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• 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

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• Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area.

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• Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering Sciences.

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• 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...