Journal of Nonlinear Mathematical Physics

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way we calculate some compatible Poisson structures on four dimensional and nilpotent six dimensional symplectic real Lie groups. Then using Magri-Morosi’s...

Based on the Lax triple (Bm, Bn, L) of the BKP and CKP hierarchies, we derive the nonlinear evolution equations from the generalized Lax equation. The solutions of some evolution equations are presented, such as soliton and rational solutions.

We present an explicit representation of an N-fold Darboux transformation T̃N for the short pulse equation, by the determinants of the eigenfunctions of its Lax pair. In the course of the derivation of T̃N, we show that the quasi-determinant is avoidable, and it is contrast to a recent paper (J. Phys....

In this paper, we are concerned with a modified complex short pulse (mCSP) equation of defocusing type. Firstly, we show that the mCSP equation is linked to a complex coupled dispersionless equation of defocusing type via a hodograph transformation, thus, its Lax pair can be deduced. Then the bilinearization...

We consider the Riemann–Hilbert method for initial problem of the vector Gerdjikov–Ivanov equation, and obtain the formula for its N-soliton solution, which is expressed as a ratio of (N + 1) × (N + 1) determinant and N × N determinant. Furthermore, by applying asymptotic analysis, the simple elastic...

The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled...

Hybrid Ermakov-Painlevé II-IV systems are introduced here in a unified manner. Their admitted Ermakov invariants together with associated canonical Painlevé equations are used to establish integrability properties.

We summarize the most featured items characterizing the semi-discrete nonlinear Schrödinger system with background-controlled inter-site resonant coupling. The system is shown to be integrable in the Lax sense that make it possible to obtain its soliton solutions in the framework of properly parameterized...