In this paper, based on the regular Korteweg–de Vries (KdV) system, we study negative-
order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs …

We give a simple geometric interpretation of the mapping of the negative KdV equation (− ψ
xx ψ) t=(ψ 2) x as proposed by Qiao and Li (2011)[26] and the Fuchssteiner equation …

We present some nonlinear partial differential equations in 2+ 1-dimensions derived from
the KdV equation and its symmetries. We show that all these equations have the same 3 …

For the first time both non-holonomic and quasi-integrable deformations are obtained for the
AB system of coupled equations. The AB system models geophysical and atmospheric fluid …

The hierarchy of equations belonging to two different but related integrable systems, the
nonlinear Schrödinger (NLS) and its derivative variant the derivative nonlinear Schrödinger …

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave
equation, which was proposed by Karasu-Kalkani et al.[31]. In this paper, we demonstrate …

The quasi-integrable KdV equation has been obtained from the corresponding deformation
of the Hamiltonian for the usual KdV system. Following suitable gauge-fixing, it has been …

The nonholonomic deformations of nonlocal integrable systems belonging to the nonlinear
Schrödinger family are studied using the bi-Hamiltonian formalism as well as the Lax pair …

Geometric Integrability of Some Generalizations of the Camassa‐Holm Equation - Christov -
2011 - International Journal of Differential Equations - Wiley Online Library Skip to Article …

Abstract The Heisenberg Spin Chain system, in the continuum limit, can be represented by
the non-linear Schrödinger equation through the Hashimoto map. Inhomogeneity induced …