Exact Solutions for (2 + 1)-Dimensional KdV-Calogero-Bogoyavlenkskii-Schiff Equation via Symbolic Computation

Li, Yan; Chaolu, Temuer

doi:10.4236/jamp.2020.82015

Cited by 5 publications

(1 citation statement)

References 35 publications

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“…Many writers have examined the solutions to this model in the literature using various methodologies. For example, the conservation laws and traveling wave solutions for a negative-order (3+1)-dimensional KdV-CBS equation [4], dynamic behavior of (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff equation [20], the Exact solutions for (2+1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff Equation via Symbolic Computation [21], two new Painlevé integrable KdV-CBS equation and new negative-order KdV-CBS equation [3], Rational solutions for the (2+1)-dimensional Modified KdV-CBS equation [22], Nonlocal symmetry, CRE solvability and solitoncnoidal solutions of the (2+1)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation [23], Structures of interaction between lump, breather, rogue and periodic wave solutions for new (3+1)dimensional negative order KdV-CBS model [24], Nonlocal symmetry, CRE solvability and solitoncnoidal solutions of the (2+1)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation [25], Painlevé integrability and analytical solutions of variable coefficients negative order KdV-Calogero-Bogoyavlenskii-Schiff equation using auto-Bäcklund transformation [26], Painlevé analysis, integrability property and multiwave interaction solutions for a new (4+1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation [27] and so on.…”

Section: Introductionmentioning

confidence: 99%

Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

Ghulam Murtaza,

Raza,

Arshed

2024

Opt Quant Electron

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In this work, we investigate a fascinating negative-order Korteweg-de Vries Calogero-Bogoyavlenskii-Schiff equation in (3+1) dimensions, which is a collection of the Korteweg-de Vries equation and the Calogero-Bogoyavlenskii-Schiff equation. It has been looked that how this model defines the interactions of long wave propagations and how it may be used in math, physics, and engineering. We have used the unified method and the singular manifold method to determine the exact traveling wave solutions to this problem. Exponential, trigonometric, rational, and hyperbolic functions are used to represent the derived traveling wave solutions. By using the traveling wave transformation, the considered nonlinear partial differential equation is transformed into an ordinary differential equation. The full derivation of the provided model using the unified methodology and singular manifold method has been added. We have supposed that the equation has a soliton solution. We have got a system of equations by arranging the resultant equations. We have extract unknown coefficients in the system using Maple software and by plugging them into the original equation new soliton solutions to the equation are obtained. The findings show that the soliton solutions generated by these methods are valid. For illustrative purposes, we provide both 3-D and 2-D graphical representations. The strategy described in this research is superior to certain others that have been used to solve the same equation in the literature, according to computational findings. It demonstrates how these answers may be very helpful in comprehending physical processes in a range of applied mathematics fields.

show abstract

Section: Introductionmentioning

confidence: 99%

Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

Ghulam Murtaza,

Raza,

Arshed

2024

Opt Quant Electron

View full text Add to dashboard Cite

show abstract

Numerical calculation and characteristics of N-periodic waves of a (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff equation in fluid physics and plasma physics

Wang,

Zhao,

Xin

2024

Nonlinear Dyn

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Diversity of soliton dynamics to (3+1)-dimensional nKdV-nCBS equation in a long wave propagation

Murtaza,

Raza,

Arshad

2023

Preprint

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In this work, we have investigated a fascinating negative-order Korteweg-de Vries CalogeroBogoyavlenskii-Schiff equation in (3+1) dimensions, which is a collection of the Korteweg-deVries equation and the Calogero-Bogoyavlenskii-Schiff equation. It has been looked that how this model defines the interactions of long wave propagations and how it may be used in math,physics, and engineering. We have used the unified method and the singular manifold method to determine the exact traveling wave solutions to this problem. Exponential, trigonometric,rational, and hyperbolic functions are used to represent the derived traveling wave solutions.By using the traveling wave transformation, the considered nonlinear partial differential equation is transformed into an ordinary differential equation. The full derivation of the provided model using the unified methodology and singular manifold method has been added. We have supposed that the equation has a soliton solution. We have got a system of equations by arranging the resultant equations. We have extract unknown coefficients in the system using Maplesoftware and by plugging them into the original equation new soliton solutions to the equation are obtained. The findings show that the soliton solutions generated by these methods are valid. For illustrative purposes, we provide both 3-D and 2-D graphical representations. The strategy described in this research is superior to certain others that have been used to solve the same equation in the literature, according to computational findings. It demonstrates how these answers may be very helpful in comprehending physical processes in a range of applied mathematics fields.

show abstract

Exact Solutions for (2 + 1)-Dimensional KdV-Calogero-Bogoyavlenkskii-Schiff Equation via Symbolic Computation

Cited by 5 publications

References 35 publications

Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

Numerical calculation and characteristics of N-periodic waves of a (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff equation in fluid physics and plasma physics

Diversity of soliton dynamics to (3+1)-dimensional nKdV-nCBS equation in a long wave propagation

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