论文信息 - Bäcklund Transformations and Exact Soliton Solutions for Some Nonlinear Evolution Equations of the zs/akns Systemfn1fn1Communicated by Prof. M. Wadati.

Bäcklund Transformations and Exact Soliton Solutions for Some Nonlinear Evolution Equations of the zs/akns Systemfn1fn1Communicated by Prof. M. Wadati.

Abstract The general form of the Backlund transformations (BTs) for some nonlinear evolution equations (NLEEs) solvable by the inverse scattering method of Zakharov-Shabat/Ablowitz-Kaup-Newell-Segur (ZS/AKNS) and the ZS/AKNS wave functions corresponding to the soliton solutions of these NLEEs are considered. The method of characteristics is used and BTs are employed to generate new solutions from the old. Thus, families of new solution classes for the KdV equation, the mKdV equation, the sinh-Poisson equation, the Liouville equation, the stable nonlinear Schrodinger equation, the unstable nonlinear Schrodinger equation, and the inhomogeneous nonlinear Schrodinger equation are obtained.

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

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

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

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

[5] Two-dimensional magnetohydrodynamic equilibria , 1988 .

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

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

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

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

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

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

[12] M. Ablowitz,et al. Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

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