Binary Darboux Transformation and Quasideterminant Solutions of The Chiral Field

Abstract

The standard binary Darboux transformation is composed and is used to obtain exact multisoliton solutions of the chiral field model in two dimensions. The solutions are expressed in terms of quasideterminants. It has been shown that the standard binary Darboux transformation is equivalent to the elementary binary Darboux transformation.

Darboux Transformation and Soliton Solutions for a Nonlocal Two-Component Complex Modified Korteweg–de Vries Equation

“…Under the transformation (10), the Lax pairs ( 7) is changed to where We can prove that the matrixes U [1] and V [1] have the same structures with the matrixes U and V, that is and the relationship between P [1] and P is Next, we give the proof of the DT. We rewrite the Ω(Δ 1 , Δ 1 ) as then the matrix operator T has following form…”

“…Let Δ 1 = (Φ 1 , Ψ 1 ) . Basing on [9][10][11][12], we take the transformation of eigenfunction, where…”

Binary Darboux Transformation for the Supersymmetric Principal Chiral Field Model

“…We also related these solutions with the solutions obtained by Mikhailov using the dressing method [30]. We also constructed the standard binary Darboux transformation of principal chiral model in two dimensions and expressed the grammian type multisoliton solutions in terms of quasideterminants in another work [24].…”

“…In this paper we use the method employed in [24] and construct the standard binary Darboux transformation to find the exact multisolitons of supersymmetric chiral field model in two dimensions. The binary Darboux transformation is one of the well known techniques used to construct grammian type multisolitons of integrable systems [31][32][33][34].…”

Soliton solutions for a two-component generalized Sasa-Satsuma equation

“…which is also called a Sasa-Satsuma equation. Equation (4) has been extensively studied by different methods, such as inverse scattering transform [7,8], Darboux transformation [9][10][11][12][13][14] and Hirota bilinear method [15,16].…”