Exact Solutions with Jacobi Elliptic Functions of Two Nonlinear Models for Ion-Acoustic Plasma Waves

The periodic wave solutions of two nonlinear models for ion-acoustic plasma waves, including the mixed Korteweg–de Vries (KdV) and modified KdV equation and the (3+1)-dimensional modified Zakharov–Kuznetsov equation, are obtained by using the F -expansion method and introducing appropriate transformations. In the limiting cases, the solitary wave solutions of the equations are also obtained.

[1]  S. G. Tagare,et al.  Quasipotential analysis for ion-acoustic solitary waves and double layers in plasmas , 1998 .

[2]  A. H. Khater,et al.  Travelling wave solutions of some classes of nonlinear evolution equations in (1 + 1) and (2 + 1) dimensions 1 , 2002 .

[3]  B. Lu,et al.  Solitary wave solutions for some systems of coupled nonlinear equations , 1993 .

[4]  Zhang Jin-Liang,et al.  The periodic wave solutions for two systems of nonlinear wave equations , 2003 .

[5]  W. Malfliet Solitary wave solutions of nonlinear wave equations , 1992 .

[6]  F. Verheest Nonlinear dust Alfvén modes , 1994 .

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  H. Washimi,et al.  ON THE PROPAGATION OF ION ACOUSTIC SOLITARY WAVES OF SMALL AMPLITUDE. , 1966 .

[9]  H. Schamel A modified Korteweg-de Vries equation for ion acoustic wavess due to resonant electrons , 1973, Journal of Plasma Physics.

[10]  A. Chakrabarti,et al.  Solution of a generalized Korteweg—de Vries equation , 1974 .

[11]  A. H. Khater,et al.  Bäcklund transformations, a simple transformation and exact solutions for dust-acoustic solitary waves in dusty plasma consisting of cold dust particles and two-temperature isothermal ions , 1999 .

[12]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[13]  Mingliang Wang,et al.  Periodic wave solutions to a coupled KdV equations with variable coefficients , 2003 .

[14]  H. Schamel Stationary solitary, snoidal and sinusoidal ion acoustic waves , 1972 .

[15]  Travelling And Periodic Wave Solutions Of Some Nonlinear Wave Equations , 2004 .

[16]  Engui Fan,et al.  Double periodic solutions with Jacobi elliptic functions for two generalized Hirota–Satsuma coupled KdV systems , 2002 .

[17]  F. Verheest Nonlinear dust-acoustic waves in multispecies dusty plasmas , 1992 .

[18]  K. Das,et al.  Stability of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons , 1998, Journal of Plasma Physics.

[19]  A. Khare,et al.  Periodic solutions of nonlinear equations obtained by linear superposition , 2002, nlin/0203018.

[20]  Mingliang Wang SOLITARY WAVE SOLUTIONS FOR VARIANT BOUSSINESQ EQUATIONS , 1995 .

[21]  Mingliang Wang Exact solutions for a compound KdV-Burgers equation , 1996 .

[22]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[23]  T. Taniuti,et al.  Reductive Perturbation Method in Nonlinear Wave Propagation. I , 1968 .

[24]  M. M. Hassan Exact solitary wave solutions for a generalized KdV–Burgers equation , 2004 .

[25]  K. Das,et al.  Stability of solitary waves in a magnetized non-thermal plasma with warm ions , 1999, Journal of Plasma Physics.

[26]  E. Parkes,et al.  The derivation of a modified Zakharov–Kuznetsov equation and the stability of its solutions , 1999, Journal of Plasma Physics.

[27]  W. Hereman,et al.  The tanh method: I. Exact solutions of nonlinear evolution and wave equations , 1996 .

[28]  Paul Abbott,et al.  The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations , 2002 .

[29]  Zuntao Fu,et al.  New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations , 2001 .

[30]  P. G. Drazin,et al.  Solitons: Motion picture index , 1989 .

[31]  Zuntao Fu,et al.  New transformations and new approach to find exact solutions to nonlinear equations , 2002 .