New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

Wazwaz, Abdul‐Majid

doi:10.2478/s13531-013-0173-y

Cited by 15 publications

(15 citation statements)

References 16 publications

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“…(1) was …rst appeared in [19] in the investigation of the algebraic-geometrical solutions. As demonstrated in [20,21], there exist a strong relationship between Eq. (1) and the Korteweg-de Vries(KdV) equation.…”

Section: Introductionmentioning

confidence: 92%

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: 92%

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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“…Because, the integrable equations describe many real phenomena in the broad branches of science and engineering. There is a wide range of reliable methods that can be used to handle the integrable equations; for instance, Kudryashov methods [1][2][3][4][5][6], ansatz methods [7][8][9][10][11], simplified Hirota's method [12][13][14][15][16], linear superposition method [17][18][19], and multiple -function method [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation

et al. 2019

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The present article studies a B-type Kadomtsev-Petviashvili equation with certain applications in the fluids. Stating with the Hirota's bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type Kadomtsev-Petviashvili equation.

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“…Studying the nonlinear evolution equation arising in natural science is very important for us to understand and explain the nonlinear phenomena [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. By the analytical and numerical methods, many researchers constructed travelling wave solutions of some famous nonlinear mathematical physics equations, such as the nonlinear Schrödinger equation in nonlinear optics, the nonlinear Gross-Pitaevskii equation in the Bose-Einstein condensates, the Korteweg-de Vries (KdV) equation in fluid mechanics, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…The new (3+1)-dimensional nonlinear model that is going to be studied in this paper is given by [1]:…”

Section: Introductionmentioning

confidence: 99%

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Soliton Solutions and Conservation Laws of a (3+1)-Dimensional Nonlinear Evolution Equation

et al. 2019

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This work studies a new (3+1)-dimensional nonlinear model, which was introduced by Abdul-Majid Wazwaz in 2014. This new physical model describes the shallow-water waves and short waves in nonlinear dispersive models. Analytical traveling wave solutions including the solitons and plane wave solutions are derived by using the G /G-expansion technique. Moreover, the conserved quantities of this model are also given.

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New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

Abstract: Abstract:In this work, we introduce an extended (3+1)-dimensional nonlinear evolution equation. We determine multiple soliton solutions by using the simplified Hirota's method. In addition, we establish a variety of travelling wave solutions by using hyperbolic and trigonometric ansatze.

Cited by 15 publications

References 16 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

N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation

Soliton Solutions and Conservation Laws of a (3+1)-Dimensional Nonlinear Evolution Equation

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