Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves

Sadat, R.; Saleh, Rasha Hadi; Kassem, M.; Mousa, Mohamed M.

doi:10.1016/j.chaos.2020.110134

Cited by 16 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figures 1-7 depict the dynamics of some well-known solutions in the form of soliton solutions, bell-shaped solitons, triple solitons, combo singular solitons, breather-type waves, singular kink-shaped solitons, and novel solitary waves. The dynamics of exact soliton solutions are intensively analyzed, as follows: It has been shown that the newly established solutions of the higher-dimensional Fokas equation and the (2+1)-dimensional BS equation obtained using the current proposed method (which is a generalized exponential rational function technique) differ from the works of other authors, who have commonly used the analytic techniques reported in [38][39][40][41][42][43][47][48][49][50]. The solutions we obtained in this study are completely novel and more generalized exact solutions than the previous results.…”

Section: Physical Interpretation Of the Obtained Solutionsmentioning

confidence: 99%

“…Geng et al [43] recently obtained the Abel-Jacobi coordinates and the scattering coordinates. Localized solitary waves, multiple solitons, breather types, lump types, rough waves, and the interaction solutions of the (4+1)-D Fokas equation have been studied in [44][45][46][47][48][49][50]. In addition, the dynamical structures of solitons, lump types, rough waves, solitary waves, kink waves, and interaction solutions of the (2+1)-D BS equation have been investigated in [51][52][53].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

Kumar¹,

Niwas²,

Osman³

et al. 2021

Commun. Theor. Phys.

View full text Add to dashboard Cite

The prime objective of this paper is to explore the new exact soliton solutions to the higherdimensional nonlinear Fokas equation and (2+1)-dimensional breaking soliton equations via a generalized exponential rational function (GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons, double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons, elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.

show abstract

Section: Physical Interpretation Of the Obtained Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

Kumar¹,

Niwas²,

Osman³

et al. 2021

Commun. Theor. Phys.

View full text Add to dashboard Cite

show abstract

“…Therefore, search for efficient solution methods has gained more and more attention. To date, there are several effective methods that have been commonly used by mathematicians, such as Darboux transformation, [1,2] Bäcklund transformation, [3][4][5] Lie group method, [6][7][8][9] inverse scattering method, [10] Hirota bilinear method, [11][12][13][14] and hyperbolic method. [15] Among them, the Hirota bilinear method proposed by Hirota is a straightforward method for finding exact solutions of NLEEs.…”

Section: Introductionmentioning

confidence: 99%

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

2023

View full text Add to dashboard Cite

This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method. The equation is proved to be Painlevé integrable by Painlevé analysis. On the basis of the bilinear form, the forms of two-soliton solutions, three-soliton solutions and four-soliton solutions are studied specifically. The appropriate parameter values are chosen and the corresponding figures are presented. The breather waves solutions, lump solutions, periodic solutions and the interaction of breather waves solutions and soliton solutions, etc are given in this article. In addition, we also analysed the different effects of the parameters on the figures. The figures of the same set of parameters in different planes are presented to describe the dynamical behaviour of solutions. These are important for describing water waves in nature.

show abstract

“…Later, Galas, Ibrgimov, Kotz, and Patera also did many developmental jobs on the construction of the highdimensional optimal system. It is easier to solve the exact solutions of NPDEs on the basis of the optimal system, and scholars have put forward many methods that can be used to find exact solutions of NPDEs, such as the CK method [8], classical Lie group method [9][10][11][12][13][14][15], exp-function method [16], Hyperbolic method [17], and Darboux transformation [18][19][20][21], etc.These methods are widely used to find the exact solutions of NPDEs.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis, conservation laws and exact solutions for variable-coefficients (2+1)-dimensional dissipative long-wave system

2023

View full text Add to dashboard Cite

The Lie symmetry analysis, optimal system, exact solutions and conservation laws of the (2+1)-dimensional variable coefficients dissipative long-wave (vcDLW) system are introduced in this paper. Lie symmetry analysis method is used to obtain the vector field firstly. And the Olver's method is used to obtain the optimal system of one-dimensional subalgebras of the equations. Based on the optimal system, the equations are similarly reduced. Some representative equations are selected from the equations obtained after similarLY reduction, and then the (G'/G) −expansion method is applied to these equations, so that some new exact solutions of the (2+1)-dimensional vcDLW equations can be obtained. Finally, we study the conservation laws of the system.

show abstract

Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves

Cited by 16 publications

References 24 publications

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

Lie symmetry analysis, conservation laws and exact solutions for variable-coefficients (2+1)-dimensional dissipative long-wave system

Contact Info

Product

Resources

About