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

Socpus ID

84947046993 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84947046993

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