The soliton solutions and combined solutions of a high-dimensional wave soliton equation

Wang, Shaofu

doi:10.1088/1402-4896/aca055

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…For attaining the complex one soliton solution of Equation (), it is assumed the solution of Equation () as [59]:

G = 1 + {italicIe}^{θ_{1}}, I = \sqrt{- 1},

with

θ_{1} = m_{1} x + n_{1} y + k_{1} z + w_{1} t + θ_{1}^{0} .

…”

Section: The Complex Multiple Soliton Solutionsmentioning

confidence: 99%

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Wang,

Shi,

et al. 2024

Math Methods in App Sciences

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This research mainly concerned with some new solutions of the (3 + 1)‐dimensional nonlinear evolution equation (NEE). First, we extract the resonant multiple soliton solutions (RMSSs) by taking advantage of the linear superposition principle (LSP) and weight algorithm (WA). Then the non‐singular complexiton and singular complexiton solutions are developed by introducing pairs of the conjugate parameters. Besides, the complex multiple‐soliton solutions are also explored with the aid of the bilinear approach. The graph descriptions of the attained solutions are paraded to show the dynamical properties. The outcomes of this work are all new and are desirous to bring some new perspective to the investigation of the complexiton solutions to the other partial differential equations (PDEs).

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“…For attaining the complex one soliton solution of Equation (), it is assumed the solution of Equation () as [59]:

G = 1 + {italicIe}^{θ_{1}}, I = \sqrt{- 1},

with

θ_{1} = m_{1} x + n_{1} y + k_{1} z + w_{1} t + θ_{1}^{0} .

…”

Section: The Complex Multiple Soliton Solutionsmentioning

confidence: 99%

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Wang,

Shi,

et al. 2024

Math Methods in App Sciences

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New exact solitary waves for the Sasa-Satsuma model with variable coefficients

Liu,

Duan

2024

Phys. Scr.

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In this paper, we investigate the variable coefficients Sasa-Satsuma model, which can describe the propagation of a light pulse in a cylindrical fiber. We study this model and obtain rich solutions using two separate methods. We obtain analytical Weierstrass elliptic function solutions using the Weierstrass elliptic function expansion method. Some Jacobi elliptic function solutions are obtained using the modified Jacobi elliptic function expansion method. When the Jacobi elliptic function degenerates, we obtain the corresponding trigonometric, hyperbolic function solutions and periodic solutions. We also try to take the coefficients of the equation as some functions and obtain some more complicated exact solutions, which have not appeared in previous studies. Finally, we simulate some waveform diagrams of the solutions using the computer software Mathematica and obtain periodic waves, bright and dark soliton, double solitons and some complex periodic waves. With these waveform diagrams, we can observe the dynamical behavior of the solutions more clearly.

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Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions

AlBaidani,

Ali,

Ganie

2024

Open Physics

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The fractional-order differential equations (FO-DEs) faithfully capture both physical and biological phenomena making them useful for describing nature. This work presents the stable and more effective closed-form traveling-wave solutions for the well-known nonlinear space–time fractional-order Burgers equation and Lonngren-wave equation with additional terms using the exp ( − Φ ( ξ ) ) (-\Phi (\xi )) expansion method. The main advantage of this method over other methods is that it provides more accuracy of the FO-DEs with less computational work. The fractional-order derivative operator is the Caputo sense. The transformation is used to reduce the space–time fractional differential equations (FDEs) into a standard ordinary differential equation. By putting the suggested strategy into practice, the new closed-form traveling-wave solutions for various values of parameters were obtained. The generated 3D graphical soliton wave solutions demonstrate the superiority and simplicity of the suggested method for the nonlinear space–time FDEs.

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The soliton solutions and combined solutions of a high-dimensional wave soliton equation

Cited by 3 publications

References 25 publications

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

New exact solitary waves for the Sasa-Satsuma model with variable coefficients

Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions

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