Electron. J. Diff. Equ., Vol. 2015 (2015), No. 255, pp. 1-18.

Unification of integrable q-difference equations

Burcu Silindir, Duygu Soyoglu

Abstract:
This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions by utilizing Hirota direct method. Furthermore, we present that the generalized q-difference soliton equation reduces to q-analogues of Toda, KdV and sine-Gordon equations equipped with their three-q-soliton solutions by appropriate

Submitted September 3, 2015. Published October 2, 2015.
Math Subject Classifications: 37K10, 37K40, 39A13, 39A14.
Key Words: Integrability; q-soliton solutions; q-difference KdV equation; q-difference-q-difference Toda equation; q-difference.

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Burcu Silindir
Department of Mathematics
Dokuz Eylul University, Tınaztepe Campus
35160, Buca, Izmir, Turkey
email: burcusilindir@gmail.com
Duygu Soyoglu
Department of Mathematics
Izmir University of Economics
35330, Balcova, Izmir, Turkey
email: duygusoyoglu@gmail.com

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