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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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The generalized dressing method with applications to the integration of variable-coefficient Toda equations; pp. 93–98

(Full article in PDF format) doi: 10.3176/proc.2010.2.06


Authors

Hui-Hui Dai, Ting Su

Abstract

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.

Keywords

variable-coefficient Toda equation, generalized dressing method, integrability.

References

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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.
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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.
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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.
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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.
 
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Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
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