Muhammad Younis

Optical solitons in (n + 1) dimensions with Kerr and power law nonlinearities

The paper studies the dynamics of optical solitons in (n + 1)-dimensional nonlinear Schrodinger equation with Kerr and power law nonlinearities that describe the propagation of light pulses in optical fibers. First time the dark and singular optical solitons are extracted in (n + 1) dimensions. The (G′/G)-expansion scheme is used to analyze these solutions. Additionally, the constraint conditions for the existence of the solutions are also listed. However, the scheme fails to retrieve the bright soliton.

Bright, dark, and singular solitons in magneto-electro-elastic circular rod

In this article, the bright, dark, and singular solitons are being constructed for nonlinear longitudinal wave equation with dispersion caused by transverse Poisson’s effect in a magneto-electro-elastic circular rod. The solitary wave ansatz is used to carry out these solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. This article provides a lot of encouragement for the researchers in this era.

Solitary wave and shock wave solitons to the transmission line model for nano-ionic currents along microtubules

In this letter, the solitary wave and shock wave solitons for nonlinear equation of special interest in nanobiosciences, namely the transmission line model for nano-ionic currents along microtubules, have been constructed successfully. The solitary wave ansatz is used to carry out the solutions which shows the consistency.

New and more general traveling wave solutions for nonlinear Schrödinger equation

An extended Fan sub-equation method is used to seek some new and more general traveling wave solutions of nonlinear Schrödinger equation (NLSE). The important fact of this method is to take the full advantage of clear relationship among general elliptic equation involving five parameters and other existing sub-equations involving three parameters. It is preferable to use this method to solve NLSE because this method gives us all the solutions obtained previously by the application of at least four methods (the method of using Riccati equation, or auxiliary ordinary differential equation method, or first kind elliptic equation or the generalized Riccati equation as mapping equation) in a unified manner. So it is shown that this method is concise and its applications are promising.

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.

Construction of m-point binary approximating subdivision schemes

Abstract In this paper, an algorithm to construct m -point (for any integer m > 1 ) binary approximating subdivision schemes has been developed using the Cox–de Boor recursion formula. Some properties like symmetry of basis functions and polynomial reproduction are also discussed. It can be observed that most of the existing binary approximating schemes (corner cutting scheme developed by Chaikin, and 3-point, 4-point, 5-point and 6-point schemes introduced by Siddiqi and Ahmad) are either special cases or can be reproduced by the proposed algorithm.

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

On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients

Abstract The article studies the dynamics of solitons in electrical microtubule model, which describes the propagation of waves in nonlinear dynamical system. Microtubules are not only a passive support of a cell but also they have highly dynamic structures involved in cell motility, intracellular transport and signaling. The underlying model has been considered with constant and variable coefficients of time function. The solitary wave ansatz has been applied successfully to extract these solitons. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of these models.

Solitary wave and shock wave solutions of(1+1)-dimensional perturbedKlein-Gordon,(1+1)-dimensionalKaup-Keperschmidt and (2+1)-dimensionalZK-BBM equations

Abstract In this paper, two different types of envelope solitons: solitary wave and shock wave have been obtained for the (1+1)-dimensional perturbed Klein-Gordon, (1+1)- dimensional Kaup-Keperschmidt and (2+1)-dimentional ZK-BBM equations using the solitary wave ansatz. The parameter regimes, for the existence of the solitons are identified during the derivation of the solution. Since, the nonlinear wave is one of the fundamental object of nature and a growing interest has been given to the propagation of nonlinear wave in dynamical system.

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.