Darboux Transformations for the Supersymmetric Two-Boson Hierarchy

Niu, Xiaoxing; Liu, Q. P.; Xue, Lingling

doi:10.1007/s10440-022-00511-z

Cited by 2 publications

(1 citation statement)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…People often solve NLEEs to understand the phenomena behind the equations. For this reason, many methods for solving the exact solutions of NLEEs have been proposed, such as similarity reduction method 1 , Riemann-Hilbert approach 2 , homogeneous balance method 3 , (G ′ /G)-expansion method 4 , Riccati equation expansion method 5 , variable separation approach 6 , tanh method 7 , bilinear neural network method 8 , darboux transformation method 9 , Jacobi elliptic function method 10 , positive quadratic function method 11 and so on. With the continuous development of these methods, researchers have obtained many exact solutions to important nonlinear evolution equations [12][13][14][15] , greatly promoting the development of nonlinear science [16][17][18][19][20] .…”

mentioning

confidence: 99%

Soliton structures for the (3 + 1)-dimensional Painlevé integrable equation in fluid mediums

Liu

2024

Sci Rep

View full text Add to dashboard Cite

The (3 + 1)-dimensional Painlevé integrable equation are a class of nonlinear differential equations with special properties, which play an important role in nonlinear science and are of great significance in solving various practical problems, such as many important models in fields such as quantum mechanics, statistical physics, nonlinear optics, and celestial mechanics. In this work, we utilize the Hirota bilinear form and Mathematica software to formally obtain the interaction solution among lump wave, solitary wave and periodic wave, which has not yet appeared in other literature. Additionally, using the $$(G'/G)$$ ( G ′ / G ) -expansion method, we provide a rich set of exact solutions for the (3 + 1)-dimensional Painlevé integrable equation, which includes two functions with arbitrary values. This method is the first to be applied to the (3 + 1)-dimensional Painlevé integrable equation. By giving some 3D graphics and density maps, the dynamic properties are analyzed and demonstrated, which is beneficial for promoting understanding and application of the (3 + 1)-dimensional Painlevé integrable equation.

show abstract