Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity

Sajid, Naila; Perveen, Zahida; Sadaf, Maasoomah; Akram, Ghazala; Abbas, Muhammad; Abdeljawad, Thabet; Alqudah, Manar A.

doi:10.1007/s40314-022-02047-2

Cited by 19 publications

(6 citation statements)

References 28 publications

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“…Searching for the exact solutions to NEEs has always been a research hotspot for many scholars. Up to now, many effective and powerful approaches have been proposed, such as the Bäcklund transformation technique [9][10][11][12], variational technique [13,14], Sardar-subequation approcah [15,16], Darboux transformation approach [17][18][19], Kudryashov approach [20,21], exp-function approach [22,23], tanhfunction method [24,25], (G′/G)-expansion technique [26,27], unified solver approach [28,29] and so on [30][31][32][33][34][35][36]. In this study, we are going to look into the (3+1)-dimensional NEE as [37]:…”

Section: Introductionmentioning

confidence: 99%

Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Wang

2024

Phys. Scr.

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This research aims to explore some novel solutions to the (3+1)-dimensional nonlinear evolution equation (NEE) for the shallow-water waves. The resonant Y-type soliton (YTS) and X-type soliton (XTS) solutions are derived by applying the novel resonant conditions on the N-soliton solutions(N-SSs) which are extracted via the Hirota bilinear approach. Additionally, some novel and interesting hybrid interaction solutions like the interaction between Y-type soliton and 1-soliton, interaction between Y-type soliton and 1-breather solution, interaction between the Y-type soliton and the soliton molecule on the (x,y)-plane, and interaction between the X-type soliton and 1-soliton are also ascertained. The dynamic attributes of the obtained solutions are described graphically to unveil their physical behaviors. The findings in this work can help us better apprehend the nonlinear dynamics of the considered equation.

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Section: Introductionmentioning

confidence: 99%

Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Wang

2024

Phys. Scr.

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“…Solitons have important applications in physical and mathematical sciences, such as fluid mechanics, optics, elasticity and plasma science [1][2][3][4][5][6][7][8][9][10][11][12][13]. Recently, many new methods have emerged for exploring the soliton solutions of the PDEs, for instance, the Jacobi elliptic-function technique [14,15], general integral approach [16,17], trial equation approach [18,19], Bäcklund transformation approach [20], exp-function approach [19,21,22], Sardar-subequation method [23][24][25], extended F-expansion approach [26][27][28], Kudryashov's method [29][30][31] and so on [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. They are also used in scattering light waves, neural networks, and quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Wang,

Shi

2024

Phys. Scr.

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The central target of this work is to extract some novel exact solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) for the incompressible fluid. By applying the weight algorithm (WA) and linear superposition principle (LSP), we construct two sets of the complexiton solutions, which are the non-singular complexiton and singular complexiton solution via introducing the pairs of the conjugate parameters. In addition, we also explore the complex N-soliton solutions (CNSSs) via the Hirota bilinear equation (HBE) that is developed by the Cole-Hopf transform (CHT). The outlines of the corresponding exact solutions are presented graphically. As far as the information currently available, the derived solutions in this exploration are all new and are expected to enable us to investigate the dynamic characteristics of the considered equation better.

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“…They also have numerous applications in the fields of science, biomathematics, engineering, biomedical, and other fields [5][6][7][8]. For finding the analytical solutions to these NLPDEs, various methods have been developed such as Painlevé analysis [9,10], auto-Bäcklund transformation [9,10], exp-function method [11], tanh-function method [12], simplified Hirota's method [13,14], Lie symmetry analysis [15], the (G /G)-expansion method [16], Paul-Painlevé approach (PPA) method [17][18][19][20][21] and so on.…”

mentioning

confidence: 99%

“…Therefore, the solution of eq. ( 6) will be truncated as (11) where K 0 , K 1 , K 2 and N are the arbitrary unknown constants whose values have to be determined. Also, V (X) satisfies the Riccati equation of the form V X − KV 2 = 0, and the value of V (X) is given by eq.…”

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confidence: 99%

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Propagation of two-wave solitons depending on phase-velocity parameters of two higher-dimensional dual-mode models in nonlinear physics

Singh

Ray

2023

EPL

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Nonlinear evolution equations exhibit a variety of physical behaviours, which are clearly illustrated by their exact solutions. In this view, this article is concerned with the study of dual-mode (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) and Zakharov-Kuznetsov (ZK) equations. These models describe the propagation of two-wave solitons traveling simultaneously in the same direction and with mutual interaction dependent on an embedded phase-velocity parameter. The considered nonlinear evolution equations have been solved analytically for the ﬁrst time using the Paul-Painlevé approach method. As a result, new abundant analytic solutions have been derived successfully for both the considered equations. The 3D dynamics of each of the solution has been plotted by opting suitable constant values. These graphs show the dark-soliton, bright-soliton, complex dual-mode bright-soliton and complex dual-mode dark-soliton solutions.

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Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity

Cited by 19 publications

References 28 publications

Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Propagation of two-wave solitons depending on phase-velocity parameters of two higher-dimensional dual-mode models in nonlinear physics

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