Exact solutions of the time-fractional extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Ma, Hongcai; Su, Nan; Deng, Aiping

doi:10.1007/s11071-024-09318-z

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…Nonlinear partial differential equations (NLPDEs) and their fractional forms are highly useful for the purpose of modeling. The study of nonlinear phenomena covers various fields across the applied and natural sciences [3,4]. These equations provide comprehensive and clear understanding of the analyzed physical phenomena, allowing for accurate predictions of their future propagation.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of fractional solitonic profiles to multicomponent Gross–Pitaevskii system

Younas,

Yao

2024

Phys. Scr.

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The fractional multicomponent Gross-Pitaevskii system arising in the Bose-Einestein condensate is under consideration. The Gross-Pitaevskii equation plays a significant role in Bose-Einstein condensation and engineering, where it characterizes the dynamics of the condensate wave function. Superfluidity and superconductivity are two characteristics of the low-temperature phenomenon that are linked to the Bose–Einstein condensate, which is generated by a diluted atomic gas. The investigation of multi-component equations has garnered considerable attention because of their capacity to clarify intricate physical phenomena and reveal the dynamic configurations of localized wave solutions. A variety of solutions have been secured in various forms, including bright, dark, singular, and combo solitons, in addition to solutions of hyperbolic, periodic, and exponential functions. For the purpose of ensuring the solutions, recently developed integration tools called the modified Sardar subequation method and enhanced modified extended tanh-expansion method have been implemented. In nonlinear dispersive media, solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The proposed approaches are certainly the most direct, efficient, and valuable method for dealing with multiple nonlinear models that arise in applied physics and mathematics, with the purpose of generating various types of exact solutions. In addition, 3D, 2D, contour, and density plots have been utilized to visually represent the obtained results, facilitating a greater understanding of the physical effects of the derived solutions. The solutions attained are of great importance with regard to their applicability across a wide range of quantum systems.

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Section: Introductionmentioning

confidence: 99%

Dynamics of fractional solitonic profiles to multicomponent Gross–Pitaevskii system

Younas,

Yao

2024

Phys. Scr.

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Analytical solutions and molecule states of the (3+1)-dimensional variable coecient Date-Jimbo-Kashiwara-Miwa equation

Ma,

Su,

Deng

2024

Phys. Scr.

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In the article, the (3+1)-dimensional variable coefficient Date-Jimbo-Kashiwara-Miwa (vcDJKM) equation is researched systematically. The Hirota bilinear method is utilized to construct $N$-soliton solutions and by imposing appropriate condition, the resonant $Y$-type solitons and the mixed solutions formed from resonant $Y$-type solitons are obtained. In addition, the positive quadratic function is exploited to search for lump solutions as well as the new degenerating breather method is employed to derive lump solutions. More importantly, with the help of velocity resonant principle, soliton molecules, breather molecules and lump molecules can be derived. Considering various forms of variable coefficients, these obtained solutions with all kinds of shapes, including $S$-type, parabolic-type and periodic-type are demonstrated by three-dimensional graphics, density and contour plots. And the results of this research can further advance the investigation of nonlinear partial differential equations with variable coefficients.

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Exact solutions of the time-fractional extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Cited by 2 publications

References 39 publications

Dynamics of fractional solitonic profiles to multicomponent Gross–Pitaevskii system

Dynamics of fractional solitonic profiles to multicomponent Gross–Pitaevskii system

Analytical solutions and molecule states of the (3+1)-dimensional variable coecient Date-Jimbo-Kashiwara-Miwa equation

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