Integrable variable-coefficient 2D Toda lattice equations are proposed by utilizing a generalized version of the dressing method. Compatibility conditions are given, which ensures that these equations are integrable. Further, soliton solutions for the new type of equations are shown in explicit forms.
1. Zakharov, E. and Shabat, A. B. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem I. Funct. Anal. Appl., 1974, 8, 226–238.
doi:10.1007/BF01075696
2. Zakharov, E. and Shabat, A. B. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem II. Funct. Anal. Appl., 1979, 13, 13–22.
3. Chowdhury, R. and Basak, S. On the complete solution of the Hirota–Satsuma system through the dressing operator technique. J. Phys. A, 1984, 17, L863–L868.
doi:10.1088/0305-4470/17/16/001
4. Dye, J. M. and Parker, A. An inverse scattering scheme for the regularized long-wave equation. J. Math. Phys., 2000, 41, 2889–2904.
doi:10.1063/1.533278
5. Parker, A. A reformulation of the dressing method for the Sawada–Kotera equation. Inverse Problems, 2001, 17, 885–895.
doi:10.1088/0266-5611/17/4/321
6. Dai, H. H. and Jeffrey, A. The inverse scattering transforms for certain types of variable coefficient KdV equations. Phys. Lett. A, 1989, 139, 369–372.
doi:10.1016/0375-9601(89)90579-3
7. Jeffrey, A. and Dai, H. H. On the application of a generalized version of the dressing method to the integration of variable-coefficient KdV equation. Rend. Mat., Serie VII, 1990, 10, 439–455.
