Variable-coefficient F-expansion method and its application to nonlinear Schrödinger equation

Abstract In this paper, using the variable-coefficient F-expansion method, we present a number of Jacobian elliptic function solutions of nonlinear Schrodinger equations with variable-coefficient. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric function solutions, respectively. Each of these solutions exists for a certain relation between the parameters of the equation. Therefore, they are particular cases of the complete set of periodic and localized solutions which may exist for this equation. In fact, they can serve as a seeding set of solutions which could be useful in other optical studies.

[1]  Elena G. Shapiro,et al.  Variational Approach to the Design of Optical Communication Systems with Dispersion Management , 1998 .

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

[3]  James P. Gordon,et al.  Experimental observation of picosecond pulse narrowing and solitons in optical fibers (A) , 1980 .

[4]  Periodic and optical soliton solutions of the quintic complex Swift–Hohenberg equation , 2002, nlin/0209052.

[5]  Ying Zhang,et al.  Localized excitations in (2+1)-dimensional systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  A. Peacock,et al.  Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients. , 2003, Physical review letters.

[8]  Chaotic dynamical behaviour in soliton solutions for a new (2+1)-dimensional long dispersive wave system , 2003 .

[9]  Roger H.J. Grimshaw,et al.  Slowly varying solitary waves. II. Nonlinear Schrödinger equation , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  Francesco Matera,et al.  Nonlinear Optical Communication Networks , 1998 .

[11]  Li Biao,et al.  Symbolic Computation and Construction of Soliton-Like Solutions to the (2+1)-Dimensional Breaking Soliton Equation , 2003 .

[12]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[13]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[14]  E. Fan,et al.  Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation , 2001 .

[15]  V. A. Semenov,et al.  A single-mode fiber with chromatic dispersion varying along the length , 1991 .

[16]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

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

[18]  N. J. Smith,et al.  Soliton transmission using periodic dispersion compensation , 1997 .

[19]  Wenrui Xue,et al.  A new approach to exact soliton solutions and soliton interaction for the nonlinear Schrödinger equation with variable coefficients , 2004 .

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

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

[22]  M. Wadati,et al.  Solitons in Electron Beam Plasma , 1990 .

[23]  Akira Hasegawa,et al.  Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .

[24]  Yong Chen,et al.  On exact solutions of the nonlinear Schrdinger equations in optical fiber , 2004 .

[25]  E. M. Dianov,et al.  Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines , 1991 .