![](/images/graphics-bg.png)
Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-12
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
Using bifurcation method of dynamical systems, we investigate the nonlinear waves for the generalized Zakharov equations utt-cs2uxx=β(|E|2)xx, iEt+αExx-δ1uE+δ2|E|2E+δ3|E|4E=0, where α,β,δ1,δ2,δ3, and cs are real parameters, E=E(x,t) is a complex function, and u=u(x,t) is a real function.
We obtain the following results.
(i) Three types of explicit expressions of nonlinear waves are obtained, that is, the fractional expressions, the trigonometric expressions, and the exp-function expressions.
(ii) Under different parameter conditions, these expressions represent symmetric and antisymmetric solitary waves, kink and antikink waves, symmetric periodic and periodic-blow-up waves, and 1-blow-up and 2-blow-up waves.
We point out that there are two sets of kink waves which are called tall-kink waves and low-kink waves, respectively.
(iii) Five kinds of interesting bifurcation phenomena are revealed.
The first kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up and 2-blow-up waves.
The second kind is that the 2-blow-up waves can be bifurcated from the periodic-blow-up waves.
The third kind is that the symmetric solitary waves can be bifurcated from the symmetric periodic waves.
The fourth kind is that the low-kink waves can be bifurcated from four types of nonlinear waves, the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves.
The fifth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.
We also show that the exp-function expressions include some results given by pioneers.
American Psychological Association (APA)
Li, Shaoyong& Liu, Rui. 2013. Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-19.
https://search.emarefa.net/detail/BIM-504840
Modern Language Association (MLA)
Li, Shaoyong& Liu, Rui. Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations. Abstract and Applied Analysis No. 2013 (2013), pp.1-19.
https://search.emarefa.net/detail/BIM-504840
American Medical Association (AMA)
Li, Shaoyong& Liu, Rui. Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-19.
https://search.emarefa.net/detail/BIM-504840
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504840