Jacobi elliptic function solutions of the generalized Zakharov–Kuznetsov equation with nonlinear dispersion and t-dependent coefficients

Abstract An indirect F-function method is introduced to solve the Zakharov–Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients. Taking advantage of the elliptic equation, this F-function is used to map the solution of the Zakharov–Kuznetsov equation to those of the elliptic equation. As a result, we obtain exact spatiotemporal periodic traveling solutions. Two forms of this model are studied. The constraint relation between these time-dependent coefficients is established for the Jacobi elliptic function solutions to exist. This equation is then investigated with generalized evolution.

[1]  Gabriel F. Calvo,et al.  Exact solutions for the quintic nonlinear Schrödinger equation with time and space modulated nonlinearities and potentials , 2009 .

[2]  Abdul-Majid Wazwaz,et al.  BRIGHT AND DARK SOLITON SOLUTIONS FOR A K (M, N) EQUATION WITH T-DEPENDENT COEFFICIENTS , 2009 .

[3]  Milivoj Belić,et al.  Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation. , 2008, Physical review letters.

[4]  J. Weinberg,et al.  On The Existence of Stationary States of the Mesotron Field , 1940 .

[5]  W. Jr. Pauli,et al.  Zur Quantenmechanik des magnetischen Elektrons , 1927 .

[6]  Emmanuel Yomba,et al.  Construction of new solutions to the fully nonlinear generalized Camassa-Holm equations by an indirect F function method , 2005 .

[7]  Alan R. Bishop,et al.  Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology , 1980 .

[8]  Juan Belmonte-Beitia,et al.  Localized nonlinear waves in systems with time- and space-modulated nonlinearities. , 2008, Physical review letters.

[9]  Different physical structures of solutions for two related Zakharov–Kuznetsov equations , 2008 .

[10]  Sheng Zhang,et al.  Application of Exp-function method to a KdV equation with variable coefficients , 2007 .

[11]  Lin Yi,et al.  Analytical solutions to the (3+1)-dimensional generalized nonlinear Schrödinger equation with varying parameters , 2009 .

[12]  Mingliang Wang,et al.  The periodic wave solutions for the Klein–Gordon–Schrödinger equations , 2003 .

[13]  Yehuda B. Band,et al.  Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation , 1996, patt-sol/9612004.

[14]  S D Zhu,et al.  Exp-function Method for the Hybrid-Lattice System , 2007 .

[15]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[16]  D. Bazeia,et al.  Solitons with cubic and quintic nonlinearities modulated in space and time. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  A. Green.  Velocity dependent nuclear forces and their effect in nuclear matter , 1962 .

[18]  Xiangzheng Li,et al.  Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations , 2005 .

[19]  A. Biswas.  1-Soliton solution of the generalized Zakharov–Kuznetsov equation with nonlinear dispersion and time-dependent coefficients , 2009 .

[20]  Abdul-Majid Wazwaz,et al.  Explicit travelling wave solutions of variants of the K(n, n) and the ZK(n, n) equations with compact and noncompact structures , 2006, Appl. Math. Comput..

[21]  Juan Belmonte-Beitia,et al.  Solitons for the cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients , 2009 .