Sasa Satsuma Equation Research Articles

New optical soliton solutions and dynamic behaviours analysis of the Sasa-Satsuma equation in optical fibers

This article investigates novel exact solutions of the Sasa-Satsuma equation for describing the nonlinear characteristics of pulse transmission in optical fiber communication. Various new exact solutions of the Sasa-Satsuma equation were derived employing both the ( G ′ G ′ + G + A ) expansion method and the Bernoulli ( G ′ G ) expansion method. To provide a more intuitive depiction of the optical solitons’ behaviour during transmission, we generated two-dimensional graphs, three-dimensional graphs, and contour maps corresponding to the solutions. These images enable us to showcase the dynamic behaviour of this theoretical model and delve into the specific influence of the self-steepening effect on the transmission characteristics of optical solitons described by the new exact solutions to the Sasa-Satsuma equation.

Optical solitons with conformable fractional evolution for the (3+1)-dimensional Sasa–Satsuma equation

Optical solitons with conformable fractional evolution for the (3+1)-dimensional Sasa–Satsuma equation

Inverse scattering transform for the Sasa–Satsuma equation: multiple-pole case of N pairs

Inverse scattering transform for the Sasa–Satsuma equation: multiple-pole case of N pairs

Study on the fractional Sasa–Satsuma equation of optical solitons in optical fibers and telecommunications

Study on the fractional Sasa–Satsuma equation of optical solitons in optical fibers and telecommunications

Painlevé analysis of the Sasa–Satsuma equation

The Sasa-Satsuma equation is considered. The Painlevé test for partial differential equations with application of the Kruskal variable is used to investigate the necessary condition of integrability of the equation. It is shown that the equation does not pass the Painlevé test in the general case. However, there exist constraints on parameters of the equation, when all Fuchs indices are integers. In these cases the Laurent series expansions of the solution exit and, consequently, there exist analytical solutions of this partial differential equation. We confirm that there are two integrable cases, at which the Sasa–Satsuma equation passes the Painlevé test. We also obtain that there is another set of parameter values at which the equation can be an integrable.

Multi-geometric discrete spectral problem with several pairs of zeros for Sasa–Satsuma equation

Sasa–Satsuma equation is proposed to model the propagation and interaction of the sub-picosecond or femtosecond pulses in a monomode optical fiber. Different from several integrable equations in the Ablowitz–Kaup–Newell–Segur system, the higher-order zeros of Riemann–Hilbert problem for the Sasa–Satsuma appear in quadruples. A new approach to study the multi-geometric discrete spectral problem with several pairs of zeros for the Sasa–Satsuma equation is proposed. Thus, the complete soliton solutions corresponding to the higher-order zeros with arbitrary geometric and algebraic multiplicities are derived. Moreover, the inelastic interactions between or among the solitons corresponding to the higher-order non-elementary zeros exhibit the shape-changing phenomena.

Solitons with varying amplitudes and/or varying velocities in a variable-coefficient mixed spectral generalized Sasa–Satsuma equation revealed through the Riemann–Hilbert method

The integrable Sasa–Satsuma (SS) equation, a higher-order Nonlinear Schrödinger (NLS)-type model, has important applications in the field of optics. In this study, we present a generalized SS equation with variable coefficients derived from a mixed spectral problem, abbreviated as vcmsgSSE, and construct its N-soliton solution using the Riemann–Hilbert (RH) method. First, we provide the Lax pair associated with the vcmsgSSE and perform a spectral analysis on it, which allows us to derive a solvable RH problem. Then, by solving this RH problem we construct an explicit expression for N-soliton solution of the vcmsgSSE. Finally, under a special reduction, we obtain the specific one-soliton solution and two-soliton solution of the vcmsgSSE, and use them to illustrate graphically the N-soliton solution with varying amplitude and/or varying velocity corresponds to the physical background of non-uniform medium assumed by the vcmsgSSE.

Correction to: Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

Correction to: Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

The Sasa–Satsuma equation with high-order discrete spectra in space-time solitonic regions: soliton resolution via the mixed ∂¯ -Riemann–Hilbert problem

In this paper, we investigate the Cauchy problem of the Sasa–Satsuma (SS) equation with initial data belonging to the Schwartz space. The SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3 × 3 Lax representation. With the aid of the ∂¯ -nonlinear steepest descent method of the mixed ∂¯ -Riemann–Hilbert problem, we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

New traveling wave solutions for generalized Sasa–Satsuma equation via two integrating techniques

New traveling wave solutions for generalized Sasa–Satsuma equation via two integrating techniques

Simple and high-order N-solitons of the nonlocal generalized Sasa–Satsuma equation via an improved Riemann–Hilbert method

Simple and high-order N-solitons of the nonlocal generalized Sasa–Satsuma equation via an improved Riemann–Hilbert method

Highly dispersive optical solitons with differential group delay for Sasa-Satsuma equation having multiplicative white noise

AbstractThis paper is about the retrieval of highly dispersive optical solitons for Sasa-Satsuma equation with differential group delay in presence of white noise. There are four integration schemes that make this retrieval possible. A full spectrum of optical solitons have been revealed from these schemes. The parametric restrictions for the existence of such solitons are also presented. The displayed surface plots support the analytical findings.

The Dynamical Behavior Analysis and the Traveling Wave Solutions of the Stochastic Sasa–Satsuma Equation

The Dynamical Behavior Analysis and the Traveling Wave Solutions of the Stochastic Sasa–Satsuma Equation

Soliton unveilings in optical fiber transmission: Examining soliton structures through the Sasa–Satsuma equation

The exploration of higher-order and multicomponent extensions of the nonlinear Schrödinger equation holds significant importance across diverse applications, notably within the field of optics. Among these equations, the integrable Sasa–Satsuma equation stands out for its captivating soliton solutions. The Sasa–Satsuma equation serves as a mathematical representation for describing the propagation of femtosecond light pulses through optical fibers. The breather, multiwave, combined dark–bright, singular, dark, bright and periodic singular optical soliton solutions are derived in this paper by using the 1φ(ϑ),φ′(ϑ)φ(ϑ) and multivariate generalized exponential rational integral function approach. Furthermore, the paper emphasizes the essential fiber parameters essential for the emergence of these structures and offers visual representations of chosen solutions to elucidate their physical characteristics. The novelty of this work lies in the inaugural application of these methods to the Sasa–Satsuma equation and gives a significant advancement in the understanding of optical phenomena. This study not only opens avenues for further research but also introduces a fresh perspective on the Sasa–Satsuma model in the field of nonlinear physics with its applications in optical systems.

Geometric realization of the Sasa-Satsuma equation on the symmetric space SU(3)/U(2)

The analytic property of the Sasa-Satsuma equation has been well-explored via using an array of mathematical tools (such as the inverse scattering transformation, the Hirota bilinear method and the Darboux transformation). This paper devotes to exploring geometric properties of this equation via the zero curvature representation in terms of the language in Yang-Mills theory. The generalized Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the symmetric Lie algebra g=k⊕m with initial data being suitably restricted is gauge equivalent to the Sasa-Satsuma equation. This gives a geometric realization of the Sasa-Satsuma equation.

Analytical investigation of space–time shifted nonlocal stochastic Sasa–Satsuma equation using the enhanced modified extended tanh-expansion method for stochastic solitary waves Solutions

In this paper, discover exact solutions of the space–time shifted nonlocal stochastic Sasa–Satsuma equations using the enhanced modified extended tanh-expansion method. This method is a sophisticated mathematical approach for analytical and approximate solution of a nonlinear partial differential equations. The space–time shifted nonlocal stochastic Sasa–Satsuma equations define the behavior of two complex-valued functions, u and v, in a nonlinear system. These equations are complicated to solve analytically because they contain a number of components that describe space–time shifting, nonlocal interactions, and stochastic problems. To increase reliability and effectiveness of the solutions, this method couples the extended tanh-function method with an enhanced method. In order to demonstrate how white noise affects the solutions to the space–time shifted nonlocal stochastic Sasa–Satsuma equations, we also use Matlab to create 3D surfaces and contour graphs of exact solutions.

Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

A Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line

A Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line

Optical solitons and other wave solutions to fractional-order nonlinear Sasa–Satsuma equation in mono-mode optical fibers using IM extended tanh function method

Optical solitons and other wave solutions to fractional-order nonlinear Sasa–Satsuma equation in mono-mode optical fibers using IM extended tanh function method

Soliton solutions and a bi-Hamiltonian structure of the fifth-order nonlocal reverse-spacetime Sasa-Satsuma-type hierarchy via the Riemann-Hilbert approach

<p>Our objective is to explore the intricacies of a nonlinear nonlocal fifth-order scalar Sasa-Satsuma equation in reverse spacetime which is rooted in a nonlocal $ 5 \times 5 $ matrix AKNS spectral problem. Starting with this spectral problem, we derive both local and nonlocal symmetry relations through rotations within a defined group. We then formulate a specific type of Riemann-Hilbert problem, facilitating the generation of soliton solutions. These solutions are generated by utilizing vectors that reside in the kernel of the matrix Jost solutions. Under the condition where reflection coefficients are null, the jump matrix reduces to the identity, leading to soliton solutions via the corresponding Riemann-Hilbert problem. The explicit formulas of these soliton solutions enable a comprehensive exploration of their dynamics.</p>