In this article, the applications of Power Index Method (PIM) are presented to ascertain function solutions AKNS equation. We find out adequate explicit general for in form exponential, trigonometric, and logarithmic functions which have their importance physical sciences. used transformations indexes independent variables nonrestricted parameters. During our investigation, we seen that nonline...

In this paper, we obtain some exact solutions of Derivative Reaction-Diffusion (DRD) system and, as by-products, we also show some exact solutions of DNLS via Hirota bilinearization method. At first, we review some results about two by two AKNS-ZS system, then introduce Hirota bilinearization method to find out exact N-soliton solutions of DNLS and exact N-dissipaton solutions of the Derivative...

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). We also show that the RTC is gauge equivalent to the discrete AKNS hierarchy and the unitary matrix model. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. The simple approach to the discrete RTC hierarchy based o...

Abstract The Landau-Ginzburg-Higgs (LGH) equation explains the ocean engineering models, superconductivity and drift cyclotron waves in radially inhomogeneous plasma for coherent ion-cyclotron waves. In this paper, with a simple modification of Ablowitz-Kaup-Newell-Segur (AKNS) formalism, integrability LGH is proved by deriving Lax pair. Hence that, inverse scattering transformation (IST) appli...

Abstract We relate the scattering theory of focusing AKNS system with equally sized nonvanishing boundary conditions to that matrix Schrödinger equation. This (shifted) Miura transformation converts nonlinear (NLS) equation into a new nonlocal integrable apply triplet method solving Marchenko integral equations by separation variables derive multisoliton solutions this equation, thus proposing ...

Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, r-matrices and integrals of motion in involution are explicitly proposed for the resulting constrained systems in the cases of the first four orders. The obtained integrals of motion are proved to be functionally independent and thus th...