Yu Toda Sasa Fukuyama Equation Research Articles

Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

Breather and soliton solutions of a generalized (3 + 1)-dimensional Yu–Toda–Sasa–Fukuyama equation

Fluid mechanics is a branch of physics that focuses on the study of the behavior and laws of motion of fluids, including gases, liquids, and plasmas. The Yu–Toda–Sasa–Fukuyama equation, a class of Kadomtsev–Petviashvili type equations, is a significant integrable model with applications in fluids and other fields. In this paper, we study breather and soliton solutions of a generalized (3 + 1)-dimensional YTSF equation. By utilizing the Hirota bilinear method and Painlevé analysis, we construct solutions in the form of trigonometric and hyperbolic functions and analyze the interaction between waves graphically. We consider the characteristics of wave distribution along characteristic lines to obtain the distance between each wave and the angle generated, which is beneficial for understanding the ocean wave superposition effect. Additionally, we examine the dynamic characteristics of the wave, such as amplitude, velocity, period, shape, position, width, and phase. Furthermore, we investigate the effects of the system parameters on solitons and breathers.

Dynamic investigation to the generalized Yu–Toda–Sasa–Fukuyama equation using Darboux transformation

Dynamic investigation to the generalized Yu–Toda–Sasa–Fukuyama equation using Darboux transformation

Variety of solutions and dynamical behavior for YTSF equations

We construct non-homogeneous polynomial lump wave solutions of the Yu-Toda-Sasa-Fukuyama (YTSF) equation, based on a bilinear approach, enriching the formal diversity of lump waves. By studying the interaction between the lump solutions of the YTSF equation and the solitary wave solutions, we find a new aggregation effect and elastic collision effect. We obtain exact solutions, such as the solution of separated variables and periodic nonlinear wave solutions, by applying the Lie symmetry group method and the bilinear method.
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The impact of the Wiener process on solutions of the potential Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid

The impact of the Wiener process on solutions of the potential Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid

The Analytical Stochastic Solutions for the Stochastic Potential Yu–Toda–Sasa–Fukuyama Equation with Conformable Derivative Using Different Methods

We consider in this study the (3+1)-dimensional stochastic potential Yu–Toda–Sasa–Fukuyama with conformable derivative (SPYTSFE-CD) forced by white noise. For different kind of solutions of SPYTSFE-CD, including hyperbolic, rational, trigonometric and function, we use He’s semi-inverse and improved (G′/G)-expansion methods. Because it investigates solitons and nonlinear waves in dispersive media, plasma physics and fluid dynamics, the potential Yu–Toda–Sasa–Fukuyama theory may explain many intriguing scientific phenomena. We provide numerous 2D and 3D figures to address how the white noise destroys the pattern formation of the solutions and stabilizes the solutions of SPYTSFE-CD.

Resonant interactions between lumps/rogue waves and solitons for the (3+1)-dimensional Yu–Toda–Sasa–Fukuyama equation

Resonant interactions between lumps/rogue waves and solitons for the (3+1)-dimensional Yu–Toda–Sasa–Fukuyama equation

Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method. The employment of the complex conjugate condition of parameters of N-soliton solutions leads to the construction of breather solutions. Then, the lump solution is obtained with the aid of the long-wave limit method. Based on the transformation mechanism of nonlinear waves, a series of nonlinear localized waves can be transformed from breathers, which include the quasi-kink soliton, M-shaped kink soliton, oscillation M-shaped kink soliton, multi-peak kink soliton, and quasi-periodic wave by analyzing the characteristic lines. Furthermore, the molecular state of the transformed two-breather is studied using velocity resonance, which is divided into three aspects, namely the modes of non-, semi-, and full transformation. The analytical method discussed in this paper can be further applied to the investigation of other complex high-dimensional nonlinear integrable systems.

Extensive novel waves evolution of three-dimensional Yu–Toda–Sasa–Fukuyama equation compatible with plasma and electromagnetic applications

There is no doubt that the investigation of the interaction and propagation of plasma and electromagnetic waves play an important role in understanding these phenomena. The three-dimensional Yu–Toda–Sasa–Fukuyama equation (YTSFE) is a competent mathematical model of waves in plasma, electromagnetics, or fluids. An optimal system of infinitesimal symmetries is constructed to discover extensive and astonishingly exact solutions to the YTSFE. The outstanding solutions include periodic, polynomials, fractional, logarithmic, exponential, hyperbolic, exponential integral, Airy and complex functions. These solutions are significant because they help understand how plasma and electromagnetic applications work at different boundary or initial conditions.

Some exact solutions of the Yu–Toda–Sasa–Fukuyama equation with time-dependent coefficients via two different methods

In the current study, the generalized (G′/G)-expansion method and a new modified simple equation method (NMSEM) have been utilized to secure the exact solutions of the Yu-Toda-Sasa-Fukuyama (YTSF) equation with time-dependent coefficients, which describes two layers of liquid (or in an elastic) media. By implementing these methods, we have secured the three different families of travelling wave solutions (such as hyperbolic, rational and trigonometric functions) of the independent variables and the arbitrary parameters of the equation. Further, the graphical representation of the solitons are done with the help of the software Maple.

Weierstrass elliptic function solutions and their degenerate solutions of (2+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Weierstrass elliptic function solutions and their degenerate solutions of (2+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Analytical study of nonlinear water wave equations for their fractional solution structures

This paper examines the three-dimensional nonlinear time-fractional water wave equations for their analytical wave solutions. These are the equations of the names [Formula: see text]-Zakharov–Kuznetsov–Burgers equation and [Formula: see text]-Yu–Toda–Sasa–Fukuyama equation. The obtained wave solutions are in the form of kink, periodic and singular waves by utilizing the [Formula: see text]-expansion approach. The aforesaid solutions are verified and demonstrated graphically via symbolic soft computations.

Analyzing study for the 3D potential Yu–Toda–Sasa–Fukuyama equation in the two-layer liquid medium

In this work, we use the (m+1/G′)-expansion method and the Adomian decomposition method to study the 3D potential Yu–Toda–Sasa–Fukuyama (3D-pYTSF) equation which has a good application in the two-layer liquid medium. For the first time, the (m+1/G′)-expansion and the Adomian decomposition methods are used to establish novel exact wave solutions and to study some numerical solutions for the 3D-pYTSF equation, respectively. Through using the analytical method, kink-type wave, singular solution and some complex solutions to the suggested equation are successfully revealed. The obtained wave solutions are represented with some figures in 3D and contour plots.

On the Exact Solutions of Nonlinear Potential Yu–Toda–Sasa–Fukuyama Equation by Different Methods

In this article, the exact solutions to the potential Yu–Toda–Sasa–Fukuyama equation are successfully examined by the extended complex method and G ′ / G -expansion method. Consequently, we find solutions for three models of Weierstrass elliptic functions, simply periodic functions, and rational function solutions. The obtained results will play an important role in understanding and studying potential Yu–Toda–Sasa–Fukuyama equation. It is observed that the extended complex method and G ′ / G -expansion method are reliable and will be used extensively to seek for exact solutions of any other nonlinear partial differential equations (NPDEs).

Analytic solutions and conservation laws of a (2+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation

This article analytically investigates a (2+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation. We secure the solutions of this equation via the engagement of Lie symmetry reductions alongside direct integration techniques. We gain non-topological 1-soliton as well as periodic function solutions of the equation. Series solution of the underlying equation is also achieved by exploiting power series technique. Furthermore, the utilization of (G′/G)-expansion method is done in procuring some closed-form solutions of the equation. Graphical exhibition of the dynamical character of the gained results is given in a bid to have a sound understanding of the physical phenomena of the underlying model. Conclusively, we give the conserved vectors of the aforementioned equation by employing both the standard multiplier approach as well as the Ibragimov’s conservation theorem.

On the solutions and conservation laws of the Yu–Toda–Sasa–Fukuyama equation of plasma physics

In this work, we investigate the two-dimensional Yu–Toda–Sasa–Fukuyama equation, which has many applications in plasma physics and other fields of study in natural sciences. Exact analytical solutions of this model are presented by invoking Lie symmetry analysis technique. Moreover, the power series expansion method is also used to construct exact analytical solutions. We present the 2D and 3D graphical representations of the obtained solutions for some parametric values so as to demonstrate the dynamic behaviour of the solutions. Furthermore, conserved vectors are derived by making use of two methods, namely the multiplier method and Noether’s theorem.

Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3$$+$$1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid or a lattice

Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3$$+$$1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid or a lattice

High-order breathers and semi-rational solutions of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation

In this paper, based on the Hirota bilinear method, the high-order breathers and interaction solutions between solitons and breathers of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation are investigated. The lump and semi-rational solutions are obtained by applying the long wave limit of the [Formula: see text]-soliton solution. Two types of semi-rational solutions are derived by choosing specific parameters, which are the mixture of the lump solution and solitons, and the mixture of the lump solution and breathers. Furthermore, the time evolution diagram illustrate the dynamic behavior of these solutions.

Multiple rogue wave solutions of (2+1)-dimensional YTSF equation via Hirota bilinear method

In present paper, multiple rogue wave solutions of (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation were studied by applying the traveling wave transformation and the Hirota bilinear method. We obtained its 1-rogue wave, 3-rogue wave, 6-rogue wave and 8-rogue wave solutions through symbolic computation. Three-dimensional, contour and density plots of corresponding solutions vividly shown the physical structure and properties. Furthermore, these solutions have greatly enriched the exact solutions of (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation on the existing literature.