Explicit solitary wave structure for the stochastic resonance nonlinear Schrödinger equation under Brownian motion with dynamical analysis.

This study, analyzed the explicit solitary wave soliton for the stochastic resonance nonlinear Schrödinger equation under the Brownian motion. The Schrödinger equations are mostly used to describe how light moves via planar wave guides and nonlinear optical fibres. Analytical technique is applied to gained the various solitary waves and soliton solutions for the resonance nonlinear Schrödinger equation namely, generalized exponential rational function method.

Impact of Brownian motion on the optical soliton solutions for the three component nonlinear Schrödinger equation.

In this manuscript, the three-component nonlinear stochastic Schrö dinger equation under the effects of Brownian motion in the Stratonovich sense is examined here. The different types of exact optical soliton solutions are explored under the noise effects. The propagation of an optical pulse in a birefringent optical fiber is described by the three nonlinear complex models.

Revealing homoclinic breather waves, periodic lump waves and other waves forms of an integrable reduced spin Hirota-Maxwell-Bloch system.

In this manuscript, we investigate various wave forms of an integrable reduced spin Hirota-Maxwell-Bloch system, which accounts for the femtosecond pulses transmitted in an erbium doped fibre. We achieved this using periodic wave and logarithmic transformations. We investigated homoclinic breather waves, periodic lump waves, mixed waves, M-shaped waves interacting with kink and rogue waves and multi waves.

Reliable numerical scheme for coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise.

In this study, we consider the coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise. The coupled nonlinear Schrödinger equation, which shows the complex envelope amplitudes of the two modulated weakly resonant waves in two polarisations and is used to describe the pulse propagation in high birefringence fibre, has several uses in optical fibres.query:Journal instruction requires a city for affiliations; however, these are missing in affiliation [6].

Breather, lump and other wave profiles for the nonlinear Rosenau equation arising in physical systems.

This work explores the mathematical technique known as the Hirota bilinear transformation to investigate different wave behaviors of the nonlinear Rosenau equation, which is fundamental in the study of wave occurrences in a variety of physical systems such as fluid dynamics, plasma physics, and materials science, where nonlinear dynamics and dispersion offer significant functions. This equation was suggested to describe the dynamic behaviour of dense discrete systems. We use Mathematica to investigate these wave patterns and obtained variety of wave behaviors, such as M-shaped waves, mixed waves, multiple wave forms, periodic lumps, periodic cross kinks, bright and dark breathers, and kinks and anti-kinks.

Regularity and wave study of an advection-diffusion-reaction equation.

In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended direct algebraic method with traveling wave transformation has been used.

Numerical study of diffusive fish farm system under time noise.

In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties.

Exact solitary wave propagations for the stochastic Burgers' equation under the influence of white noise and its comparison with computational scheme.

In this manuscript, the well-known stochastic Burgers' equation in under investigation numerically and analytically. The stochastic Burgers' equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results.

Multiwaves, breathers, lump and other solutions for the Heimburg model in biomembranes and nerves.

In this manuscript, a mathematical model known as the Heimburg model is investigated analytically to get the soliton solutions. Both biomembranes and nerves can be studied using this model. The cell membrane's lipid bilayer is regarded by the model as a substance that experiences phase transitions.

Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis.

In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel techniques used to explore the solitary wave structures namely as; generalized Riccati equation mapping and modified auxiliary equation (MAE) methods.