Analytical Construction Of Peaked Solutions For The Nonlinear Evolution Of An Electromagnetic Pulse Propagating Through A Plasma
Keywords
approximate solution; control of error; Nonlinear Schr¨odinger equation; nonlinear wave equation; pair plasmas
Abstract
We obtain analytical solutions, by way of the homotopy analysis method, to a nonlinear wave equation describing the nonlinear evolution of a vector potential of an electromagnetic pulse propagating in an arbitrary pair plasma with temperature asymmetry. As the method is analytical, we are able to construct peaked structures which propagate through the pair plasma, analogous to peakon solutions. These solutions are obtained through a novel matching of inner and outer homotopy solutions. In order to ensure that our analytical results are valid over the whole real line, we also discuss the convergence of the analytical results to the true solution, through minimization of the residual errors resulting from an approximate analytical solution. These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schr¨odinger type.
Publication Date
10-9-2015
Publication Title
Quaestiones Mathematicae
Volume
38
Issue
5
Number of Pages
725-748
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.2989/16073606.2014.981719
Copyright Status
Unknown
Socpus ID
84947046993 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84947046993
STARS Citation
Baxter, Mathew; van Gorder, Robert A.; and Vajravelu, Kuppalapalle, "Analytical Construction Of Peaked Solutions For The Nonlinear Evolution Of An Electromagnetic Pulse Propagating Through A Plasma" (2015). Scopus Export 2015-2019. 1131.
https://stars.library.ucf.edu/scopus2015/1131