Dimensional potential-YTSF Equation Research Articles

An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Abstract This paper is devoted to investigating new non-traveling wave solutions for the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. By using the generalized variable separation method and extended three-wave approach, the process of solving the (3 + 1)-dimensional potential-YTSF equation is simplified and the interactions of multiple waves are revealed. With the aid of Maple, we derive thirty-six types new exact explicit non-traveling wave solutions with a like-parabolic tail. The main characteristic of these solutions is that they contain three arbitrary functions, which greatly enrich the diversity of solutions. This characteristic shows the novelty of our work. In particular, selecting suitable arbitrary functions, we can obtain traveling solutions, such as kink-wave solutions, solitary-wave solutions, kinky breather-wave solutions, singular solutions and periodic solutions. Then, some dynamical phenomena are exhibited by 3D representation, providing the complicated structure of the non-traveling wave solutions for the (3 + 1) dimensional potential-YTSF equation and their physical interpretation. In addition, our findings improve and extend the existing literature on related topics.

Novel solitary and resonant multi-soliton solutions to the (3 + 1)-dimensional potential-YTSF equation

In this study, the (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation arising from the (3 + 1)-dimensional Kadomtsev–Petviashvili equation is investigated in detail by using two powerful approaches. First, the generalized resonant multi-soliton solution is generated via the simplified linear superposition principle. Second, after applying the simplest equation method, the generalized single solitary solution is extracted. The results show that the obtained solutions are perfect. The physical explanation of the obtained solutions is depicted in various 3D and 2D figures, which are used to illustrate that the interactions of resonant multi-soliton waves are inelastic. Ultimately, the study reveals that the inelastic interactions can be determined by the sign of the wave related number [Formula: see text].

Investigation of solitons and mixed lump wave solutions with [formula omitted]-dimensional potential-YTSF equation

The article investigates the exact and mixed lump wave solitons to the (3+1)-dimensional potential YTSF equation, which is an extension of the Bogoyavlenskii-Schif equation. Different types of interaction solutions in terms of a new merge of positive quadratic functions, trigonometric functions and hyperbolic functions are obtained, which are investigated using the extended three soliton test approach. The dynamical behavior of solutions has also depicted in different 3D representations. The representations show that the soliton solutions are obtained in the form of train and cusp. Some other solutions like lamb wave with high peak, and lump solutions with kink background are also observed in these representations.

Cross-Kink Wave Solutions and Semi-Inverse Variational Method for (3 + 1)-Dimensional Potential-YTSF Equation

Cross-Kink Wave Solutions and Semi-Inverse Variational Method for (3 + 1)-Dimensional Potential-YTSF Equation

Abundant new non-travelling wave solutions for the (3+1)-dimensional potential-YTSF equation

By combining the extended homoclinic test approach (EHTA) with the method of separation of variables explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation is constructed. With the aid of symbolic computation, abundant new explicit exact solutions of the (3+1)-dimensional potential-YTSF equation are obtained. The results obtained her e reveal the complex structure of the solutions of the (3+1) dimensional potential-YTSF equation. Many of the previous results obtained in other literature can be seen as special cases here. When some arbitrary functions included in these solutions are taken as some special functions, exact periodic solitary wave, periodic soliton, periodic cross-kink wave, periodic two-solitary wave are presented.

Bilinear approach to soliton and periodic wave solutions of two nonlinear evolution equations of Mathematical Physics

In the present paper, the potential Kadomtsev–Petviashvili equation and (3+1)-dimensional potential-YTSF equation are investigated, which can be used to describe many mathematical and physical backgrounds, e.g., fluid dynamics and communications. Based on Hirota bilinear method, the bilinear equation for the (3+1)-dimensional potential-YTSF equation is obtained by applying an appropriate dependent variable transformation. Then N-soliton solutions of nonlinear evolution equation are derived by the perturbation technique, and the periodic wave solutions for potential Kadomtsev–Petviashvili equation and (3+1)-dimensional potential-YTSF equation are constructed by employing the Riemann theta function. Furthermore, the asymptotic properties of periodic wave solutions show that soliton solutions can be derived from periodic wave solutions.

New exact solutions for the $$(3+1)$$ ( 3 + 1 ) -dimensional potential-YTSF equation by symbolic calculation

In this paper, we employ the improved homoclinic test technique and the extended homoclinic test technique. With the help of the symbolic calculation and applying the improved methods, we solve the $$(3+1)$$ -dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation to obtain some new periodic kink-wave, periodic soliton and periodic wave solutions.

利用扩展的(G'/G)展开法求(3 + 1)维YSFY势方程的精确解

利用扩展的(G'/G)展开法求(3 + 1)维YSFY势方程的精确解

Multiple soliton solutions, soliton-type solutions and rational solutions for the (3+1)-dimensional potential-YTSF equation

In this paper, we employ the extended variable-coefficient homogeneous balance method (EvcHB), the Painleve-Backlund transformation and the simplified Hirota’s method to derive auto-Backlund transformation, multiple soliton solutions and multiple singular soliton solutions of the (3+1)-dimensional potential-YTSF equation. We also obtain a variety of traveling wave solutions, soliton-type solutions and rational solutions of distinct physical structures.

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

In this article, a new extended (G′/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Exact Solutions for (3+1)-Dimensional Potential-YTSF Equation and Discrete Kadomtsev-Petviashvili Equation

By employing Hirota bilinear method, we mainly discuss the (3+1)-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get itsNexponential wave solutions. In virtue of some Riemann theta function formulas, we also construct its quasiperiodic solutions and analyze the asymptotic properties of these solutions. For the latter, by using certain variable transformations and identities of the theta functions, we explicitly investigate its periodic waves solutions in terms of one-theta function and two-theta functions.

Traveling Wave Solution of (3+1) Dimensional Potential-YTSF Equation by Bernoulli Sub-ODE Method

In this paper, we derive exact traveling wave soluti-ons of (3+1) dimensional potential-YTSF equation by a proposed Bernoulli sub-ODE method. The method appears to be efficient in seeking exact solutions of nonlinear equations. We also make a comparison between the present method and the known (G’/G) expansion method.

The Improved \(\frac{G'}{G}\)- Expansion Method for Solving \((3+1)\)-Dimensional Potential- YTSF Equation

In this paper, the improved \(\frac{G'}{G}\)-expansion method is used to construct explicit the traveling wave solutions involving parameters of the \((3+1)\)-dimensional potential-YTSF equation, where �\(G=G(\xi)\)�satisfies a second order linear differential equation. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions.

Exact periodic cross-kink wave solutions and breather type of two-solitary wave solutions for the (3 + 1)-dimensional potential-YTSF equation

In this paper, the (3+1)-dimensional potential-YTSF equation is investigated. Exact solutions with three-wave form including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave solutions are obtained using Hirota’s bilinear form and generalized three-wave approach with the aid of symbolic computation. Moreover, the properties for some new solutions are shown with some figures.

Application of the(G′G)-expansion method to (3 +1)-dimensional nonlinear evolution equations

In this paper, the (G′G)-expansion method is employed to solve the (3 +1)-dimensional Kadomtsev–Petviashvili (KP) equation, the (3 +1)-dimensional potential-YTSF equation and the (3 +1)-dimensional Jimbo–Miwa (JM) equation. Exact traveling wave solutions are obtained. The traveling wave solutions are expressed in terms of hyperbolic functions, the trigonometric functions and the rational functions.

New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized -expansion method

In this paper, we construct new traveling wave solutions of some nonlinear evolution equations in mathematical physics via the (3+1)-dimensional potential-YTSF equation, the (3+1)-dimensional modified KdV–Zakharov–Kuznetsev equation, the (3+1)-dimensional Kadomtsev–Petviashvili equation and the (1+1)-dimensional KdV equation by using a generalized -expansion method, where G = G(ξ) satisfies the Jacobi elliptic equation [G′(ξ)]2 = P(G). Here, we assume that P(G) is a polynomial of fourth order. Many new exact solutions in terms of the Jacobi elliptic functions are obtained.

New periodic soliton solutions for the (3 + 1)-dimensional potential-YTSF equation

New exact periodic kink-wave, periodic soliton and doubly periodic wave solutions for the (3 + 1)-dimensional potential-YTSF equation are obtained by using homoclinic test technique, extended homoclinic test technique, two-soliton method and bilinear form method, respectively.

Multiple-soliton solutions for the Calogero–Bogoyavlenskii–Schiff, Jimbo–Miwa and YTSF equations

In this work we employ the Hirota’s bilinear method to derive multiple-front solutions for nonlinear evolution equations. Three models, namely, the (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff equation, the (3 + 1)-dimensional Jimbo–Miwa equation, and the (3 + 1)-dimensional potential YTSF equation, are used as vehicles to conduct the analysis. The work shows the power of the bilinear method and the variety of the obtained front solutions.

Solving the (3+1)-dimensional potential – YTSF equation with Exp-function method

In this paper, the (3+1)-dimensional potential-YTSF equation is solved using the exp-function method with the aid of symbolic computation, as a result, new generalized solitary solutions and periodic solutions with free parameters are therefore obtained, and the free parameters in the obtained generalized solutions might imply some meaningful results in physical process. As special case, some known solutions acquired by the tanh-coth method in open literature are recovered due to the suitable choice of free parameters. It is shown that Exp-function method is a straight, concise, reliable and promising mathematical tool to solve nonlinear evolution equations arising in mathematical physics.

New solutions of distinct physical structures to high-dimensional nonlinear evolution equations

In this work, we employ the tanh–coth method for a reliable treatment on nonlinear evolution equations. Three models, namely the (3 + 1)-dimensional Jimbo–Miwa equation, the (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff equation, and the (3 + 1)-dimensional potential YTSF equation, are use as vehicles to conduct the analysis. New travelling wave solutions are formally derived. The work shows the power of the proposed scheme and the variety of the obtained solutions.