Dimensional Potential Yu Toda Sasa Fukuyama Research Articles

APPLICATION OF VARIATIONAL PRINCIPLE AND FRACTAL COMPLEX TRANSFORMATION TO (3+1)-DIMENSIONAL FRACTAL POTENTIAL-YTSF EQUATION

This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.

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

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].

N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

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

Multiple Lump Novel and Accurate Analytical and Numerical Solutions of the Three-Dimensional Potential Yu–Toda–Sasa–Fukuyama Equation

The accuracy of novel lump solutions of the potential form of the three–dimensional potential Yu–Toda–Sasa–Fukuyama (3-Dp-YTSF) equation is investigated. These solutions are obtained by employing the extended simplest equation (ESE) and modified Kudryashov (MKud) schemes to explore its lump and breather wave solutions that characterizes the dynamics of solitons and nonlinear waves in weakly dispersive media, plasma physics, and fluid dynamics. The accuracy of the obtained analytical solutions is investigated through the perspective of numerical and semi-analytical strategies (septic B-spline (SBS) and variational iteration (VI) techniques). Additionally, matching the analytical and numerical solutions is represented along with some distinct types of sketches. The superiority of the MKud is showed as the fourth research paper in our series that has been beginning by Mostafa M. A. Khater and Carlo Cattani with the title “Accuracy of computational schemes”. The functioning of employed schemes appears their effectual and ability to apply to different nonlinear evolution equations.

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.

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.

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.

Lump solution and its interaction to (3+1)-D potential-YTSF equation

This paper studies the $$(3+1)$$ -dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by implementing the Hirota bilinear method. As a consequence, the Hirota bilinear method is successfully employed and acquired a type of the lump solution and five types of interaction solutions in terms of a new merge of positive quadratic functions, trigonometric functions and hyperbolic functions. All solutions have been verified back into its corresponding equation by Maple. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions are trustworthy in the applied sciences.

Lump Solutions to a (3+1)-Dimensional Potential-Yu–Toda–Sasa–Fukuyama (YTSF) Like Equation

The main motivation of our article is to implement generalized bilinear differential operators to create a (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) like equation linked with prime number $$p=3$$ . Specific features of lump solutions realistically localized in all directions of the (3+1)-dimensional potential-YTSF like equation is founded from bilinear closed form of it. Six free parameters are exist in the achieved lump solutions. Among them two parameters are owing to the translation invariance of the YTSF equation and the remaining parameters suit a non-zero determinant condition. Some 3D plots and several contour plots of the lump solutions with demanding choices of the existing parameters are made to show energy distribution of the lump waves and can be used to visualize the other properties of rogue wave phenomena.

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.

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota's perturbation scheme. With the help of Maple, applying the approach to the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation yields exact explicit one-wave, two-wave and three-wave solutions, which include one-soliton, two-soliton and three-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of the two-wave and three-wave solutions.