Dimensional Potential Yu Toda Sasa Fukuyama 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.

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

The abundant mixed solutions of ($$2+1$$)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

The abundant mixed solutions of ($$2+1$$)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Periodic wave solutions and stability analysis for the (3+1)-D potential-YTSF equation arising in fluid mechanics

This paper aims at investigating the periodic wave solutions for the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation, from its bilinear form, obtained using the Hirota operator. Two major cases were studied from two different ansatzes. The 3D, 2D and density representation illustrating some cases of solutions obtained have been represented from a selection of the appropriate parameters. The modulation instability is employed to discuss the stability of got solutions. That will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics and so on.

Multiple lump solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

The bilinear method is employed to construct the multiple lump solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation in fluid dynamics. The 1-lump solutions, 3-lump solutions and 6-lump solutions are explicitly presented. The centers of the 3-lump wave have a triangular structure, and the 6-lump wave possesses a central peak and five peaks in a ring. The dynamic characteristics of the obtained solutions are analyzed with the aid of numerical simulation.

Lump-type solutions and interaction solutions in the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

In this work, we consider the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. By employing the extended homoclininc test approach and Hirota bilinear method, we derive a class of lump solutions of the potential YTSF equation. It is interesting that interaction solutions between the lump-type solution and one stripe soliton, and the lump-type solution and a pair of resonance solution are obtained, respectively, by using a direct method. The interaction solutions of the potential YTSF equation show that a lump-type solution appears from a soliton wave and swallowed by it later, which are the completely non-elastic interactions that rare to see. Moreover, we also obtain its periodic lump-type solutions. It is hoped that our results can be used to enrich the dynamic behaviors of the YTSF-type equations.

Interactional solutions of a lump and a solitary wave for two higher-dimensional equations

In this paper, by using the bilinear equation and different test functions, we obtain lump–bell solutions for the $$(4+1)$$ -dimensional Fokas equation, which describe nonelastic and elastic interactions. We consider various interactions of the lump–bell solutions including fusion, fission, catch-up and head-on. The asymptotic behaviors and dynamics of lump–bell solutions are analyzed graphically. With a scaling transformation, we also obtain the lump–kink solution which describes elastic interactions of a lump- and a kink-type wave for the $$(3+1)$$ -dimensional potential Yu–Toda–Sasa–Fukuyama equation.

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

With the aid of the symbolic computation, we present an improved ( G ′ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Solitonic interaction and Pfaffianization for a [formula omitted]-dimensional potential Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid

Under investigation in this paper is a (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation, which is used for the interfacial waves in a two-layer liquid. Based on the bilinear forms, we obtain the bilinear Bäcklund transformation which differs from those previous reported for such an equation. We obtain the N-kink soliton solutions in the Gramian. Two elastic and inelastic oblique kink solitons are shown. Two elastic parallel kink solitons are also presented. Furthermore, based on the Pfaffianization, Wronski- and Gram-type Pfaffian solutions for a Pfaffianized coupled (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama system are derived.

Dynamics of kinky wave for ( $$3+1$$ 3 + 1 )-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Exact kinky breather-wave solutions for the (\(3\,{+}\,1\))-dimensional potential Yu–Toda–Sasa–Fukuyama equation are obtained by using extended homoclinic test technique. Based on the kinky breather-wave solution, rational breather-wave solution is generated by homoclinic breather limit method. Some new dynamical features of kinky wave are presented, including kink degeneracy, rational breather wave is drowned or swallowed up by kinky wave in the interaction between rational breather wave and kinky wave. These results enrich the variety of the dynamics of higher dimensional nonlinear wave field.

A transformed rational function method for (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial differential equations.