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Article
Open AccessInvestigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior
This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, ...
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Article
Open AccessComputational study of effect of hybrid nanoparticles on hemodynamics and thermal transfer in ruptured arteries with pathological dilation
The intended research aims to explore the convection phenomena of a hybrid nanofluid composed of gold and silver nanoparticles. This research is novel and significant because there is a lack of existing studie...
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Article
Open AccessA study of self-adjointness, Lie analysis, wave structures, and conservation laws of the completely generalized shallow water equation
This article explores the analysis of the completely generalized Hirota–Satsuma–Ito equation through Lie symmetry analysis. The equation under consideration represents a more comprehensive form of the (2+1)-di...
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Article
Open AccessMulti-dimensional phase portraits of stochastic fractional derivatives for nonlinear dynamical systems with solitary wave formation
This manuscript delves into the examination of the stochastic fractional derivative of Drinfel’d-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. ...
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Article
Analysis of nonlinear dynamics of Novikov–Veselov equation using solitonic solutions, bifurcation, periodic and quasi-periodic solutions, and Poincaré section
This paper demonstrates the efficacy of the extended direct algebraic approach in generating solutions for traveling and solitary waves from higher-order nonlinear evolution equations, specifically utilizing t...
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Article
Nonlinear dynamics of the generalized unstable nonlinear Schrödinger equation: a graphical perspective
In this work, the generalized unstable nonlinear Schrödinger equation is examined, which is used to predict the temporal evolution of disturbances in marginally stable or unstable media. First, we construct Li...
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Article
Propagation of velocity profile of unsteady magnetohydrodynamics flow between two orthogonal moving porous discs
The impact of laminar, incompressible, two-dimensional magnetohydrodynamics flow influenced by a magnetic field between two orthogonal moving porous plates has been investigated. The governing model is modifie...
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Article
The weakly non-linear waves propagation for Kelvin–Helmholtz instability in the magnetohydrodynamics flow impelled by fractional theory
The weakly nonlinear wave propagation that occurs in the presence of magnetic fields, in which energy is concentrated in a narrow band of wave-numbers in a dispersive and dissipative fluid. The main objective ...
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Article
Some new wave profiles and conservation laws in a Pre-compressed one-dimensional granular crystal by Lie group analysis
In the present exploration, some new wave profiles are constructed via Lie symmetry of transformations scheme by the one-dimensional optimal system in a pre-compressed one-dimensional granular crystal. Lie gro...
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Article
New soliton solutions of Heisenberg ferromagnetic spin chain model
In the given research, our main goal is to explore new soliton solutions in \((2+1)\)
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Article
New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques
In this survey, the ionic currents along the microtubules equation handled by applying two different techniques. It describes the ionic transport throughout the intracellular environment. This phenomenon expla...
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Bifurcation of new optical solitary wave solutions for the nonlinear long-short wave interaction system via two improved models of \((\frac{G'}{G})\) expansion method
This study performs two recent methods on the nonlinear long-short wave interaction system (NLSWIS) to obtain novel formulas of solitary solutions representing an optical field that does not alter by multiplic...
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Computation of complex fields of perturbed \((2+1)\) -dimensional Schrödinger’s hyperbolic equation
In the paper, we are recovering optical solutions of the \( (2 + 1)\) ( ...
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A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas–Lenells model
In this paper, a diverse range of travelling wave structures of perturbed Fokas–Lenells model (p-FLM) is obtained by using the extended $$({G{...
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Article
Soliton solutions, soliton-type solutions and rational solutions for the coupled nonlinear Schrödinger equation in magneto-optic waveguides
The present paper aims to investigate the solitonic structures present in coupled nonlinear Schrödinger equation (NLSE). We have examined the system for generalized anticubic (AC) nonlinearty for which AC nonl...
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Article
Open AccessOptical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and M-truncated derivatives: a comparative study
In this paper, we investigate the optical solitons of the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law nonlinearity which shows various phenomena in physics like nonlinear waves, second-ord...
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Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model
The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic...
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Article
Group Classification, Reductions and Exact Solutions of a Class of Higher Order Nonlinear Degenerate Parabolic Equation
A complete group classification of the nonlinear degenerate parabolic equation is presented and symmetry generators are calculated for each f(u). For arbitrary f(u), one dimensional conjugacy classes for symmetry...
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Classification of Cosmic Scale Factor via Noether Gauge Symmetries
In this paper, a complete classification of Friedmann-Robertson-Walker (FRW) spacetime by using approximate Noether approach is presented. Considered spacetime is discussed for three different types of univers...
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Conserved quantities for the non-linear Klein–Gordon equation
In this paper, the conserved quantities of the non-linear Klein–Gordon equation \(u_{tt}=u_{xx}+f(u)\) are derived. T...
