Syed Tahir Raza Rizvi

Analytical and soliton solutions

In this article, analytical solutions and different types of soliton envelopes: bright, dark and singular for the nonlinear model, namely, nanobioelectronics transmission lines have been constructed along with constrained conditions. The modified extended tanh-function method and exp-function method have been used to find analytical solutions, and while solitary wave ansatz is used to construct these soliton solutions. Additionally, the constraint conditions, for the existence of the soliton solutions are also listed.

New Thirring optical solitons with vector-coupled Schrödinger equations in birefringent fibers

The article studies the dynamics of Thirring optical solitons in birefrigent fibers with vector-coupled nonlinear Schrödinger equations. The -expansion scheme has been used to extract the dark and singular soliton solutions along with constraint conditions. It may also be noted that a couple of other solutions known as singular periodic solutions, fall out as a by-product of this scheme

Exact solitons in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity

This work studies the optical solitons in the physical model that describes the propagation of optical solitons in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity via the (G′/ G)-expansion scheme, exact dark and singular one-soliton solutions, along with the constraint conditions, are reported.

Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity

The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.

A variety of exact solutions to (2+1)-dimensional schrödinger equation

ABSTRACT The article investigates that the -dimensional Schrödinger equation admits a rich variety of exact solutions with the range of five parameters. The solutions are of qualitatively different nature, depending on the different values of parameters. The obtained solutions are of triangular-type, soliton-type, doubly periodic-like, single and combined non-degenerate jacobi elliptic function like. Additionally, the constraint conditions for the existence of the solutions are also emerged during the derivation. The important fact of using the extended Fan sub-equation method is to take the full advantage of clear relationship among general elliptic equation involved with five parameters and other existing sub-equations involved with three parameters.

Chirped optical solitons in nanofibers

The nonlinear chirp solitons are for the first time derived in optical nanofibers, thus illustrating the set of confined structure with nontrivial phase for the model of Schrodinger–Hirota equation...

On cycle-supermagicness of subdivided graphs

Llado and Moragas [‘Cycle-magic graphs’, Discrete Math. 307 (2007), 2925–2933] showed the cyclic-magic and cyclic-supermagic behaviour of several classes of connected graphs. They discussed cycle-magic labellings of subdivided wheels and friendship graphs, but there are no further results on cycle-magic labellings of other families of subdivided graphs. In this paper, we find cycle-magic labellings for subdivided graphs. We show that if a graph has a cycle-(super)magic labelling, then its uniform subdivided graph also has a cycle-(super)magic labelling. We also discuss some cycle-supermagic labellings for nonuniform subdivided fans and triangular ladders.