NDLI: Bäcklund transformation and N-shock-wave solutions for a (3+1)-dimensional nonlinear evolution equation

Content Provider	Springer Nature Link
Author	Sun, Ya Tian, Bo Wang, Yu Feng Zhen, Hui Ling
Copyright Year	2015
Abstract	In this paper, a (3+1)-dimensional nonlinear evolution equation is investigated, which can be used to describe reacting mixtures and shallow water waves. Through the Hirota method and symbolic computation, bilinear forms and Bäcklund transformation are derived, which are different from those in the existing literature. Moreover, N-shock-wave solutions are obtained. Based on those shock-wave solutions, propagation and collision of the shock waves are discussed via the asymptotic and graphic analysis on different planes: (1) oblique elastic collisions between/among the two/three shock waves will arise on the x–y and y–z planes, while parallel elastic collisions exist on the x–z plane; (2) shock waves maintain their original directions, amplitudes and velocities except for some small phase shifts after each collision; (3) the shock wave with higher amplitude travels faster and moves across the slower.
Starting Page	851
Ending Page	861
Page Count	11
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	84
Issue Number	2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-12-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	(3+1)-Dimensional nonlinear evolution equation Hirota method Shock-wave solutions Bäcklund transformation Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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