In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Sale...In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Salerno equation). Our solutions obtained here are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinear evolution equations(NLEEs).展开更多
In this article,the fractional diffusion-advection equation with resetting is introduced to promote the theory of anomalous transport.The fractional equation describes a particle’s non-diffusive motion performing a r...In this article,the fractional diffusion-advection equation with resetting is introduced to promote the theory of anomalous transport.The fractional equation describes a particle’s non-diffusive motion performing a random walk and is reset to its initial position.An analytical method is proposed to obtain the solution of the fractional equation with resetting via Fourier and Laplace transformations.We study the influence of the fractional-order and resetting rate on the probability distributions,and the mean square displacements are analyzed for different cases of anomalous regimes.展开更多
Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,p...Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.展开更多
文摘In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Salerno equation). Our solutions obtained here are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinear evolution equations(NLEEs).
文摘In this article,the fractional diffusion-advection equation with resetting is introduced to promote the theory of anomalous transport.The fractional equation describes a particle’s non-diffusive motion performing a random walk and is reset to its initial position.An analytical method is proposed to obtain the solution of the fractional equation with resetting via Fourier and Laplace transformations.We study the influence of the fractional-order and resetting rate on the probability distributions,and the mean square displacements are analyzed for different cases of anomalous regimes.
基金the Institution of Emi-nence,University of Delhi,India,for providing financial assistance for this research through the IoE scheme under Faculty Research Programme(FRP)with Ref.No./IoE/2021/12/FRP.
文摘Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.
