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This paper proposes Polak-Ribière-Polyak (PRP) conjugate gradient (CG) directions based on two efficient scaling strategies. The first scaling parameter is determined by approaching the quasi- Newton direction, and the second by utilizing the well-known Barzilai-Borwein approach. In addition, we proposed two directions that satisfy the sufficient descent criterion regardless of the line search strategy. The proposed directions lead to a matrix-free algorithm for solving monotone-constrained nonlinear systems. The proposed algorithm's global convergence analysis is presented using some underlying assumptions. Furthermore, a detailed numerical comparison with other existing algorithms revealed that the proposed algorithm is both efficient and effective. Finally, the proposed technique is applied to the motion control problem of a two-joint planar robotic manipulator. [ABSTRACT FROM AUTHOR]

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Mart i ´ nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations. [ABSTRACT FROM AUTHOR]

This study focuses on the Ablowitz–Kaup–Newell–Segur (AKNS) water waves equation. Painleve test (P-test) will be implemented to check the integrability of AKNS equation and an extended modified auxiliary equation mapping (EMAEM) architectonic is implemented to get a new set of traveling wave solutions like periodic and doubly periodic, bell type, kink, singular kink, anti-kink, trigonometric, singular, rational, combined soliton like solutions and hyperbolic solutions. Furthermore, it is analyzed that the implemented algorithm is efficient and accurate for solving nonlinear evolution equations (NLEEs). Finally, graphical simulations (2D, 3D and contours) are also provided to illustrate the detailed behavior of the solution and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on the Davey–Stewartson (DS)-II equation, and the extended modified auxiliary equation mapping (EMAEM) architectonic is used to develop a new set of solutions such as kink, singular kink, rational, combined soliton-like solutions, bell-type solutions, trigonometric and hyperbolic solutions. Furthermore, this study reveals that the used technique is efficient for solving other nonlinear evolution equations (NLEEs). The Painleve test (P -test) will also be used to examine the integrability of the DS-II equation. Finally, graphical simulations are designed to show the exact behavior of solutions as well as the efficacy of the suggested strategy. [ABSTRACT FROM AUTHOR]

In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation for both the fast and slow modes is derived, whose properties are analyzed parametrically, focusing on the effect of nonextensive parameter, component of parallel anisotropic ion pressure, component of perpendicular anisotropic ion pressure, and magnetic field strength. The reductive perturbation technique is employed for reducing the fluid equation of the present plasma model to a Zakharov–Kuznetsov (ZK) equation. The parametric role of physical parameters on the characteristics of the symmetry planar structures such solitary waves is investigated. Furthermore, the stability of the pulse soliton solution of the ZK equation against the oblique perturbations is investigated. Furthermore, the dependence of the instability growth rate on the related physical parameters is examined. The present investigation could be useful in space and astrophysical plasma systems. [ABSTRACT FROM AUTHOR]

This study examines the dynamical equation of the modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV-ZK), which is used to describe wave propagation in a dispersive and nonlinear medium. This equation is an extension of the well-known KdV-ZK equation, which has been extensively studied in the literature. In this study, we examine the solitary wave solutions of the (3+1)-dimensional mKdV-ZK equation using two analytical techniques: the generalized exp(−ϕ(ξ))-expansion approach and the two-variable (G′/G, 1/G)-expansion techniques. As a result, novel soliton solutions in a variety of forms, including Kink- and anti-Kink-type breather waves, dark and bright solitons, Kink soliton and multi-peak solitons, etc. are attained. The solitary wave solutions (which represent the electrostatic field potential), quantum statistical pressures, electric fields and magnetic fields are accomplished with the use of software. These solutions have numerous applications in various areas of physics and other sciences. These results also have applications in electromagnetic wave propagation, nonlinear optics, and plasma physics. Graphical representations of these results have also been presented. These results demonstrate the effectiveness of the two-variable expansion strategy, which will also be useful in solving many other nonlinear models that arise in mathematical physics and several other applied sciences fields. This work contributes to the advancement of novel wave manipulation and control methods, the construction of improved photonic devices for sensing and communications, and plasma confinement in fusion devices, among other uses. [ABSTRACT FROM AUTHOR]