We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutativeâ€¦ (More)

We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopfâ€¦ (More)

We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, Ï†xt + Ï†xxxz/4 + Ï†xÏ†xz + Ï†xxÏ†z/2 + âˆ‚ âˆ’1 x Ï†zzz/4 = 0. This equation is obtained by unifying two directional generalizationâ€¦ (More)

We study the extension of integrable equations which possess the Lax representations to noncommutative spaces. We construct various noncommutative Lax equations by Laxpair generating technique andâ€¦ (More)

We study the integrable systems in higher dimensions which can be written not by the Hirota's bilinear form but by the trilinear form. We explicitly discuss about the Bogoyavlenskii-Schiff(BS)â€¦ (More)

Abstract We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2 +â€¦ (More)

The general KdV equation (gKdV) derived by T. Chou is one of the famous (1 + 1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. Inâ€¦ (More)

We study an extension of integrable equations which possess the Lax representations to noncommutative spaces. We construct various noncommutative Lax equations by Laxpair generating technique andâ€¦ (More)