Investigating lump and its interaction for the third-order evolution equation arising propagation of long waves over shallow water

Manafian, Jalil; Mohammed, Sizar Abid; Alizadeh, As’ad; Baskonus, Hacı Mehmet; Gao, Wei

doi:10.1016/j.euromechflu.2020.04.013

Cited by 41 publications

(10 citation statements)

References 43 publications

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“…Di¤erent nonlinear terms can work together to formulate such solutions [25,26] but there exist such solutions in linear model equations as well [27]. The important properties of the lump solutions are being that shapes, amplitudes, velocities of solitons after the collision with another soliton will keep and this is an elastic property of collision [28,29,30,31,32,33]. Many important techniques like Wronskian, Casoratian, Adomian decomposion method and bilinear Backlund transformations have been associated with rational function solutions [7].…”

Section: Introductionmentioning

confidence: 99%

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Yıldırım¹,

Yaşar²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we study lump-type solutions to a new extended (3+1)-dimensional nonlinear evolution equation which appears in the …eld of wave propagation in the nonlinear systems. We generate these types of solutions by considering the prime number p = 3 of the generalized Hirota bilinear operators. With the help of Maple symbolic computations, we retrieve twentytwo classes of lump-type solutions which are a special kind of rational function solutions, localized in all directions in the space and describe various dispersive wave phenomena. These lump-type solutions are derived from positive quadratic function solutions by using the generalized Hirota bilinear form of the considered model. The lump solutions are recovered along with the existence conditions: Analyticity, positivity and localization in all directions. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Lastly, the graphical simulations of the exact solutions are depicted.

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Section: Introductionmentioning

confidence: 99%

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Yıldırım¹,

Yaşar²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…In the past few decades, a lot of studies have been executed to find the new and further exact traveling wave solu-tion of space-time fractional PDEs by many research. With the collaboration of potential symbolic computer programming software, they have been appointed for researching appropriate solution to the nonlinear space-time fractional PDEs by executing powerful techniques, for example, the tan-ðϕ/2Þ expansion method, the sin-Gordon expansion method, the G′/G expansion method, and the advanced exponential expansion method [12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Pure Traveling Wave Solutions for Three Nonlinear Fractional Models

Li¹,

Soybaş

İlhan

et al. 2021

Advances in Mathematical Physics

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Three nonlinear fractional models, videlicet, the space-time fractional 1 + 1 Boussinesq equation, 2 + 1 -dimensional breaking soliton equations, and SRLW equation, are the important mathematical approaches to elucidate the gravitational water wave mechanics, the fractional quantum mechanics, the theoretical Huygens’ principle, the movement of turbulent flows, the ion osculate waves in plasma physics, the wave of leading fluid flow, etc. This paper is devoted to studying the dynamics of the traveling wave with fractional conformable nonlinear evaluation equations (NLEEs) arising in nonlinear wave mechanics. By utilizing the oncoming exp − Θ q -expansion technique, a series of novel exact solutions in terms of rational, periodic, and hyperbolic functions for the fractional cases are derived. These types of long-wave propagation phenomena played a dynamic role to interpret the water waves as well as mathematical physics. Here, the form of the accomplished solutions containing the hyperbolic, rational, and trigonometric functions is obtained. It is demonstrated that our proposed method is further efficient, general, succinct, powerful, and straightforward and can be asserted to install the new exact solutions of different kinds of fractional equations in engineering and nonlinear dynamics.

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“…(2) and also to study the (3 + 1)-dimensional Benjamin-Ono equation, we developed Eq. (3), to employ the Kudryashov method [13,14] as a powerful integration method for treating various nonlinear evolution equations (see also [15][16][17][18][19][20][21][22][23] for other methods). The Kudryashov method and its modified versions have been investigated by capable authors in the plenty of nonlinear models such as the nonlinear differential equations [24], higher-order local and nonlocal nonlinear equations in optical fibers [25], some (2 + 1)-dimensional nonlinear evolution equations [26], exact traveling wave solutions of the PHI-four equation, and the Fisher equation [27].…”

Section: Introductionmentioning

confidence: 99%

On the Exact Solitary Wave Solutions to the New ( $2 + 1$ ) and ( $3 + 1$ )-Dimensional Extensions of the Benjamin-Ono Equations

Zhang

Manafian

2021

Advances in Mathematical Physics

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In this paper, the Kudryashov method to construct the new exact solitary wave solutions for the newly developed ( 2 + 1 )-dimensional Benjamin-Ono equation is successfully employed. In the same vein, also the new ( 2 + 1 )-dimensional Benjamin-Ono equation to ( 3 + 1 )-dimensional spaces is extended and then analyzed and investigated. Different forms of exact solitary wave solutions to this new equation were also determined. Graphical illustrations for certain solutions in both equations are provided. We alternatively offer that the determining method is general, impressive, outspoken, and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering.

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Investigating lump and its interaction for the third-order evolution equation arising propagation of long waves over shallow water

Cited by 41 publications

References 43 publications

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Pure Traveling Wave Solutions for Three Nonlinear Fractional Models

On the Exact Solitary Wave Solutions to the New ( $2 + 1$ ) and ( $3 + 1$ )-Dimensional Extensions of the Benjamin-Ono Equations

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Investigating lump and its interaction for the third-order evolution equation arising propagation of long waves over shallow water

Cited by 41 publications

References 43 publications

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Pure Traveling Wave Solutions for Three Nonlinear Fractional Models

On the Exact Solitary Wave Solutions to the New ( 2 + 1 ) and ( 3 + 1 )-Dimensional Extensions of the Benjamin-Ono Equations

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Product

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On the Exact Solitary Wave Solutions to the New ( $2 + 1$ ) and ( $3 + 1$ )-Dimensional Extensions of the Benjamin-Ono Equations