arXiv subjects

Solomon Manukure

Publications and source records attributed to Solomon Manukure.

4 recordsLinked to original sources

arXiv2023

Explicit lump and line rogue wave solutions to a modified Hietarinta equation

Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these solutions may lead to rogue wave solutions. In this article, we study lump and rogue wave solutions of a new nonlinear non-evolutionary equation in 2+1 dimensions with the aid of a computer algebra system. We present illustrative examples and analyze the dynamical behavior of the solutions using graphical representations

nlin.SI↗

arXiv2022

Riemann-Hilbert problems for a nonlocal reverse-spacetime Sasa-Satsuma hierarchy of a fifth-order equation and its soliton solutions

We aim to present and analyze a nonlinear nonlocal reverse-spacetime fifth-order scalar Sasa-Satsuma equation, based on a nonlocal $5 \times 5$ matrix AKNS spectral problem. Starting from a nonlocal matrix AKNS spectral problem, local and nonlocal symmetry relations are derived from a group of rotations. A kind of Riemann-Hilbert problem is formulated, which allows to generate soliton solutions by using vectors lying in the kernel of the matrix Jost solutions. When reflection coefficients are zeros, the jump matrix is the identity and the corresponding Riemann-Hilbert problem yields soliton solutions, whose explicit formulas enable us to explore their dynamics.

nlin.SI↗

arXiv2019

A note on Dickson polynomials of the third kind and Legendre functions

In this paper, we show that the Dickson polynomials of the third kind satisfy a nonhomogeneous second order linear ordinary differential equation whose general solution contains Legendre functions.

math.CA↗

arXiv2014

A counterpart of the WKI soliton hierarchy associated with so(3,R)

A counterpart of the Wadati-Konno-Ichikawa (WKI) soliton hierarchy, associated with so(3,R), is presented through the zero curvature formulation. Its spectral matrix is defined by the same linear combination of basis vectors as the WKI one, and its Hamiltonian structures yielding Liouville integrability are furnished by the trace identity.

nlin.SI↗