In this article, the ratio-dependent prey-predator system perturbed with time noise is numerically investigated. It relates to population densities of prey and predator in an ecological system. The initial models only depend on a couple differential equations. We are considering model where interaction influenced by both space need for coupled nonlinear partial equation effect random behavior environment. existence solutions guaranteed using Schauder's fixed point theorem. computation...

This article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed multiplicative time noise. The numerical solutions of governing model are carried out proposed non-standard finite difference (SNSFD) scheme. stability scheme is proved by using Von-Neumann criteria and consistency shown in mean square sense. To seek exact solutions, we applied Sardar subequation (SSE) modified exponential rational functional (MERF) techniques. constructed form exponential, hyperbolic,...

This article deals with the Fitzhugh–Nagumo equation in presence of stochastic function. A numerical scheme has been developed for solution such equations which preserves certain structure unknown functions, also we have given stability analysis, consistency problem, and explicitly optimal a priori estimates existence solutions equations. unique guaranteed. The corresponding explicit function spaces are formulated form theorems. Lastly, one important feature is simulation proposed 2D 3D...

In this paper, the higher dimensional generalized Korteweg-de-Varies–Zakharov–Kuznetsov (gKdV-ZK) equation is under investigation. This model used in field of plasma physics which describes effects magnetic on weak ion-acoustic wave. We have applied two techniques, called as ϕ6-model expansion method and Hirota bilinear (HBM) to explore diversity wave structures. The solutions are expressed form hyperbolic, periodic Jacobi elliptic function (JEF) solutions. Moreover, solitary also extracted....

This paper is a key contribution with respect to the applications of solitary wave solutions unique solution in presence auxiliary data. Hence, this study provides an insight for selection solitons physical problems. Additionally, novel numerical scheme developed compare result. Further, deals stochastic Fisher-type equation numerically and analytically time noise process. The nonstandard finite difference proposed. stability analysis consistency proposed are constructed help Von Neumann Itô...

Abstract This study deals with the stochastic Fitz-Hugh Nagumo (FHN) equation and its multiple soliton solutions. The underlying model has numerous applications in neuroscience that express pulse behavior of neurons. In general, different kinds noise affect neurons, e.g., oscillations opening closing ion stations within cell membranes fluctuations conductivities system. fluctuation creates a sequence excitation. Various are branching Brownian motion process, flame propagation, nuclear...

Abstract In this study, we give the numerical scheme to stochastic nonlinear advection diffusion equation. This models is considered with white noise (or random process) having same intensity by changing frequencies. Furthermore, stability and consistency of proposed are also discussed. Moreover, it concerned about analytical solutions, Riccati equation mapping method adopted. The different families single (shock singular) mixed (complex solitary-shock, shock-singular, double-singular) form...

In this study, generalized higher-order nonlinear Schrödinger equation is under consideration analytically. This used in the field of slowly varying envelope electric optical fiber with self-phase modulation, third-order dispersion, self-steepening and stimulated Raman scattering. For sake solitons other solutions, we use two methods such as exponential rational function (GERFM) Sardar subequation method (SSEM). The solutions are gained different forms bright, dark, singular, combo solitons,...

Abstract In this study, we investigate the abundant soliton solutions for time-fractional stochastic Gray-Scot (TFSGS) model analytically. The is considered under influence of M-truncated derivative and multiplicative time noise. This a reaction–diffusion chemical concentration that explains irreversible reaction process. applied fractional version while Brownian motion taken in sense novel mathematical technique used to obtain families solutions. These are explored form shock, complicated...

This paper examines the stability analysis and exact solitary wave solutions of nonlinear partial differential equation known as Heimburg model. The several types solutions, soliton Jacobi elliptic doubly periodic function are explored by using extended Sinh-Gordon expansion approach. These investigations exhibit system’s astounding diversity waveforms, highlighting its potential applications in nerves biomembranes. By selecting some appropriate values for parameters, 3D, 2D, corresponding...

In this paper, the Allen–Cahn equation with time noise is under consideration. The extended fan-sub technique used to find exact solutions. solutions are successfully extracted in form of hyperbolic, trigonometric and mixed forms solitons. Importantly, physical unique value problems discussed using different values parameters. 2D, 3D, their corresponding contour behaviors these depicted by choosing stability controlled through Borel coefficient term.

In this paper, the time incapable illimitable paraxial wave equation which is used in Kerr-media being investigated. The has important applications light beam interaction within ripple unit and also calculation of emission outside fluctuation. We have applied two techniques, namely, He’s variational Hirota bilinear techniques to extract diversity optical structures. solutions include three-wave hypothesis, periodic cross kink, lump periodic, mixed type breather wave. 3D, 2D, their...

Abstract In this article, stochastic behavior of reaction diffusion brusselator model is under consideration. There are many physical phenomena which related to chemical concentrations. One concentration coincide with the other and their inter-diffusion a major question be addressed understood. So, that why Brusselator very proto-type standard lays foundation any kind matter concentrations different substances. It also has application in species as well. That we considering such model. The...

<abstract><p>This article deals with coupled nonlinear stochastic partial differential equations. It is a reaction-diffusion system, known as the Gray-Scott model. The numerical approximation of model discussed proposed forward Euler (SFE) scheme and non-standard finite difference (NSFD) scheme. Both schemes are consistent given system linear stability analysis discussed. SFE conditionally stable NSFD unconditionally stable. convergence also in mean square sense. simulations...

The stochastic Newell–Whitehead–Segel in [Formula: see text] dimensions is under consideration. It represents the population density or dimensionless temperature and it discusses how stripes appear temporal spatial dimensional systems. equation (NWSE) has applications different areas such as ecology, chemical, mechanical, biology bio-engineering. important thing if we problem two-dimensional (2D) manifold, then whole 3D picture can be included model. space embedded compactly 2D manifolds....

In this study, the abundant families of multiwave structures are constructed for (2 + 1)‐dimensional Sakovich model. The single and combined wave observed in shock, complex solitary‐shock, shock‐singular, periodic‐singular forms. rational solutions also emerged during derivation. new modified extended direct algebraic (NMEDA) technique mathematica software used to obtained solutions. results very useful study verify analytical with numerical experimental work nonlinear dynamics. Moreover,...

In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE a universal governing model that helps in evolution of complex fields are used dispersive media. For numerical solution, we stochastic forward Euler (SFE) scheme. To find exact solutions, chose techniques namely [Formula: see text]-model expansion. analysis proposed scheme, checked stability scheme help Von-Neumann criteria consistency mean Ito’s...

In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE a universal governing model that helps in evolution of complex fields are used dispersive media. For numerical solution, we stochastic forward Euler (SFE) scheme. To find exact solutions, chose techniques namely [Formula: see text]-model expansion. analysis proposed scheme, checked stability scheme help Von-Neumann criteria consistency mean Ito’s...

Abstract In the current study, fish farm model perturbed with time white noise is numerically examined. This contains and mussel populations external food supplied. The main aim of this work to develop time-efficient numerical schemes for such models that preserve dynamical properties. stochastic backward Euler (SBE) Implicit finite difference (SIFD) are designed computational results. mean square sense, both consistent underlying von Neumann stable. has various equilibria points all these...