Lie group analysis for a higher-order Boussinesq-Burgers system

Liu, Fei-Yan; Gao, Yi–Tian

doi:10.1016/j.aml.2022.108094

Cited by 64 publications

(4 citation statements)

References 16 publications

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“…Our objective: In this paper, for equation (1), linking ρ i ʼs, we will make use of symbolic computation [29][30][31][32] to erect a Bäcklund transformation, address some solitons and present the relevant experimental support. In addition, we will employ symbolic computation to construct a family of the similarity reductions.…”

Section: ˜˜˜˜( ) ˜˜( ) ( )mentioning

confidence: 99%

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Gao

Guo

Shan

2023

Commun. Theor. Phys.

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Recent theoretical-physics efforts have been focused on the probes for nonlinear pulse waves in the variable-radius arteries. With respect to the nonlinear waves in an artery full of blood with certain aneurysm, pulses in a blood vessel or features in a circulatory system, this paper symbolically computes out an auto-Backlund transformation via a noncharacteristic movable singular manifold, certain families of the solitonic solutions as well as a family of the similarity reductions for a variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers equation. Aiming, e.g., at the dynamical radial displacement superimposed on the original static deformation from an arterial wall, our results rely on the axial stretch of the injured artery, blood as an incompressible Newtonian fluid, radius variation along the axial direction or aneurysmal geometry, viscosity of the fluid, thickness of the artery, mass density of the membrane material, mass density of the fluid, strain energy density of the artery, shear modulus, stretch ratio, etc. We also call the attention that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.

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Section: ˜˜˜˜( ) ˜˜( ) ( )mentioning

confidence: 99%

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Gao

Guo

Shan

2023

Commun. Theor. Phys.

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“…The (2 + 1) extension of the (1 + 1) model is not obtained by just adding a second order derivative in the other spatial coordinate, rather by keeping account of the sixth order spatial mixed derivatives contribution. We could consider this equation as an extension of the (2+1) Boussinesq equations of lower order or a kind of higher order Boussinesq-Burgers equation [7,13].…”

Section: Coupled Euler-lagrange Equations For the Two Fieldsmentioning

confidence: 99%

Second order Lagrangians for (2 + 1)-dimensional generalized Boussinesq equations and an extension of the Krupka-Betounes equivalent

Palese,

Zanello

2023

J. Phys.: Conf. Ser.

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“…Painlevé analysis has been used to determine whether the NLEEs are Painlevé integrable or not [12][13][14]. Researchers have committed to the analytic solutions for the NLEEs, including the lump, soliton and rogue wave solutions [15][16][17][18][19][20][21]. The lump solutions have been found to be the rational-polynomial ones that are local in all directions of the space [22].…”

Section: Introductionmentioning

confidence: 99%

Painlevé analysis and inelastic interactions of the lumps for a generalized (2+1)-dimensional Korteweg-de Vries system for the shallow-water waves

Liu,

Tian,

Gao

2024

Phys. Scr.

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Water waves, one of the common natural phenomena, are recognized as complexand often turbulent. A generalized (2+1)-dimensional Korteweg-de Vries system forthe shallow-water waves is conducted in this paper. We perform the Painlev´e analysisand find that the system is Painlev´e integrable. We study the inelastic interactions ofthe lumps for the system. We find that two lumps, which propagate along the curveswith the equal amplitude, are symmetric about the x axis before the interaction, wherex is a scaled spatial variable. After the interaction, amplitudes of the two lumps aredifferent, but in the process of moving, the lower lump gradually increases, while thehigher lump gradually decreases, and the velocities of two lumps at the infinity areequal. We observe two different inelastic interactions of the three lumps: (1) thethree lumps are symmetric in time and space, and they slowly contract (before theinteraction) and swell (after the interaction); (2) the three lumps slowly fuse and afterthe interaction they form a straight line forward, and their amplitudes are graduallyequal when t → ∞.

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Lie group analysis for a higher-order Boussinesq-Burgers system

Cited by 64 publications

References 16 publications

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Second order Lagrangians for (2 + 1)-dimensional generalized Boussinesq equations and an extension of the Krupka-Betounes equivalent

Painlevé analysis and inelastic interactions of the lumps for a generalized (2+1)-dimensional Korteweg-de Vries system for the shallow-water waves

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