Re-study on localized structures based on variable separation solutions from the modified tanh-function method
We derive variable separation solutions of the ( 1 + 1 )-dimensional KdV-type model by means of the modified tan h -function method with three different ansätz. Superficially speaking, the positive and negative power-symmetric ansatz seems to be better than the positive-power ansatz and radical sign...
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| Published in | Nonlinear dynamics Vol. 83; no. 3; pp. 1331 - 1339 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.02.2016
Springer Nature B.V |
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| Online Access | Get full text |
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| Abstract | We derive variable separation solutions of the (
1
+
1
)-dimensional KdV-type model by means of the modified tan
h
-function method with three different ansätz. Superficially speaking, the positive and negative power-symmetric ansatz seems to be better than the positive-power ansatz and radical sign combined ansatz because the positive and negative power-symmetric ansatz can construct the most forms of variable separation solutions. Actually, we find that various “different” solutions obtained by the modified tanh-function method are not independent, and many of the so-called new solutions are equivalent to one another. Moreover, in the two- or multi-component system, if we construct localized coherent structures for a special component based on variable separation solutions, we must note the structure constructed by the other component for the same equation in order to avoid the appearance of some divergent and un-physical structures. We hope that these results above contribute to the analysis on exact solutions and the construction of localized structures for other nonlinear models. |
|---|---|
| AbstractList | We derive variable separation solutions of the (
1
+
1
)-dimensional KdV-type model by means of the modified tan
h
-function method with three different ansätz. Superficially speaking, the positive and negative power-symmetric ansatz seems to be better than the positive-power ansatz and radical sign combined ansatz because the positive and negative power-symmetric ansatz can construct the most forms of variable separation solutions. Actually, we find that various “different” solutions obtained by the modified tanh-function method are not independent, and many of the so-called new solutions are equivalent to one another. Moreover, in the two- or multi-component system, if we construct localized coherent structures for a special component based on variable separation solutions, we must note the structure constructed by the other component for the same equation in order to avoid the appearance of some divergent and un-physical structures. We hope that these results above contribute to the analysis on exact solutions and the construction of localized structures for other nonlinear models. We derive variable separation solutions of the (\[1+1\])-dimensional KdV-type model by means of the modified tanh-function method with three different ansätz. Superficially speaking, the positive and negative power-symmetric ansatz seems to be better than the positive-power ansatz and radical sign combined ansatz because the positive and negative power-symmetric ansatz can construct the most forms of variable separation solutions. Actually, we find that various “different” solutions obtained by the modified tanh-function method are not independent, and many of the so-called new solutions are equivalent to one another. Moreover, in the two- or multi-component system, if we construct localized coherent structures for a special component based on variable separation solutions, we must note the structure constructed by the other component for the same equation in order to avoid the appearance of some divergent and un-physical structures. We hope that these results above contribute to the analysis on exact solutions and the construction of localized structures for other nonlinear models. We derive variable separation solutions of the (\(1+1\))-dimensional KdV-type model by means of the modified tanh-function method with three different ansaetz. Superficially speaking, the positive and negative power-symmetric ansatz seems to be better than the positive-power ansatz and radical sign combined ansatz because the positive and negative power-symmetric ansatz can construct the most forms of variable separation solutions. Actually, we find that various "different" solutions obtained by the modified tanh-function method are not independent, and many of the so-called new solutions are equivalent to one another. Moreover, in the two- or multi-component system, if we construct localized coherent structures for a special component based on variable separation solutions, we must note the structure constructed by the other component for the same equation in order to avoid the appearance of some divergent and un-physical structures. We hope that these results above contribute to the analysis on exact solutions and the construction of localized structures for other nonlinear models. |
| Author | Zhang, Yu-Peng Wang, Yue-Yue Dai, Chao-Qing |
| Author_xml | – sequence: 1 givenname: Yue-Yue surname: Wang fullname: Wang, Yue-Yue email: wangyy424@163.com organization: School of Sciences, Zhejiang A & F University – sequence: 2 givenname: Yu-Peng surname: Zhang fullname: Zhang, Yu-Peng organization: School of Sciences, Zhejiang A & F University – sequence: 3 givenname: Chao-Qing surname: Dai fullname: Dai, Chao-Qing organization: School of Sciences, Zhejiang A & F University |
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| Copyright | Springer Science+Business Media Dordrecht 2015 Nonlinear Dynamics is a copyright of Springer, (2015). All Rights Reserved. |
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| Keywords | Different ansätz Divergent structure Modified tanh-function method Korteweg–de Vries-type model |
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| Snippet | We derive variable separation solutions of the (
1
+
1
)-dimensional KdV-type model by means of the modified tan
h
-function method with three different... We derive variable separation solutions of the (\[1+1\])-dimensional KdV-type model by means of the modified tanh-function method with three different ansätz.... We derive variable separation solutions of the (\(1+1\))-dimensional KdV-type model by means of the modified tanh-function method with three different ansaetz.... |
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| SubjectTerms | Automotive Engineering Classical Mechanics Coherence Construction Control Dynamical Systems Engineering Equivalence Exact solutions Mathematical analysis Mathematical models Mathematical programming Mechanical Engineering Original Paper Queuing theory Radicals Separation Vibration |
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| Title | Re-study on localized structures based on variable separation solutions from the modified tanh-function method |
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