Bäcklund Transformations and Exact Solutions for Alfvén Solitons in a Relativistic Electron–Positron Plasma

Nonlinear Alfven waves, propagating along a homogeneous magnetic field, are studied using relativistic isotropic hydrodynamics. Alfven solitons of the moving-wave and wave packet types are considered for modified Korteweg–de Vries (mKdV) equation and the nonlinear Schrodinger (NLS) equation, respectively. The method of characteristics is used and the Backlund transformations (BTs) are employed to generate new solutions from the old ones. Thus, families of new solutions for the mKdV and the NLS equations are obtained. The question arises which solitons exist in the pulsar atmosphere.

[1]  A. Mikhailovskii,et al.  Alfven solitons in a relativistic electron-positron plasma. II. Kinetic theory , 1985 .

[2]  D. Callebaut,et al.  Heating of plasma by Alfvén waves envelope , 1994 .

[3]  P. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[4]  M. Ablowitz,et al.  The Inverse scattering transform fourier analysis for nonlinear problems , 1974 .

[5]  M. Wadati,et al.  Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws , 1975 .

[6]  Exact solutions of nonlinear evolution equations of the AKNS class , 1989, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[7]  M. Wadati,et al.  Simple Derivation of Bäcklund Transformation from Riccati Form of Inverse Method , 1975 .

[8]  Colin Rogers,et al.  Bäcklund transformations and their applications , 1982 .

[9]  A. H. Khater,et al.  Bäcklund transformations and Painlevé analysis: Exact solutions for a Grad—Shafranov-type magnetohydrodynamic equilibrium , 1997 .

[10]  P. Sulem,et al.  Plasma Heating by Alfvén Wave Filamentation: A Relevant Mechanism in the Solar Corona and the Interstellar Medium , 1997 .

[11]  F. Verheest.  Solitary Alfvén modes in relativistic electron-positron plasmas , 1996 .

[12]  A. H. Khater,et al.  Bäcklund transformations and Painlevé analysis: Exact soliton solutions for strongly rarefied relativistic cold plasma , 1997 .

[13]  Hugo D. Wahlquist,et al.  Backlund transformation for solutions of the Korteweg-de Vries equation , 1973 .

[14]  M. Wadati,et al.  The Modified Korteweg-de Vries Equation , 1973 .

[15]  A. H. Khater,et al.  Bäcklund transformations and Painlevé analysis: Exact solutions for the nonlinear isothermal magnetostatic atmospheres , 1997 .

[16]  D. Callebaut,et al.  Linear and nonlinear interaction of electromagnetic waves with weakly ionized magnetized plasmas , 1995 .

[17]  K. Porsezian.  Backlund transformations and explicit solutions of certain inhomogeneous nonlinear Schrodinger-type equations , 1991 .

[18]  J. Sakai,et al.  Nonlinear Alfven Wave in an Ultra-Relativistic Electron-Positron Plasma , 1980 .

[19]  L. Stenflo,et al.  Nonlinear propagation of electromagnetic waves in magnetized electron-positron plasmas , 1985 .

[20]  A. H. Khater,et al.  Bäcklund transformations: exact solutions for the KdV and the Calogero–Degasperis–Fokas mKdV equations , 1998 .

[21]  G. Lamb.  Bäcklund transformations for certain nonlinear evolution equations , 1974 .

[22]  A. H. Khater,et al.  Two new classes of exact solutions for the KdV equation via Bäcklund transformations , 1997 .

[23]  Hsing‐Hen Chen.  A Bäcklund transformation in two dimensions , 1975 .

[24]  M. Ablowitz,et al.  Nonlinear-evolution equations of physical significance , 1973 .

[25]  M. Wadati,et al.  The Exact Solution of the Modified Korteweg-de Vries Equation , 1972 .

[26]  A. Mikhailovskii,et al.  Alfven solitons in a relativistic electron-position plasma. I. Hydrodynamic theory , 1985 .

[27]  An extremely diluted asymmetric network with graded response neurons , 1991 .

[28]  Chuan-Sheng Liu,et al.  Bäcklund transformation solutions of the Toda lattice equation , 1975 .