N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material

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.

show abstract

“…By the way, other relevant solitonic issues might be found in [43][44][45][46][47][48][49][50][51][52][53].…”

Section: Experimental Supportmentioning

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.

View full text Add to dashboard Cite

show abstract

“…In this section, we shall provide an N -fold DT of System (1) using Lax Pair (2). We begin by introducing a gauge transformation [21,22]…”

Section: N -Fold Dt Of System (1)mentioning

confidence: 99%

Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformations and solitons

Shen

Tian

Zhou

et al. 2023

Preprint

View full text Add to dashboard Cite

Ferromagnetic materials such as the ferrites are used in the electronic and energy industries. Here, we concentrate on a complex Kraenkel-Manna-Merle system for the ultra-short waves in a ferrite. An N-fold Darboux transformation of that system is presented via an existing Lax pair, where N is a positive integer. A generalized (1, N − 1)- fold Darboux transformation, which admits one spectral parameter, and a generalized (m, N − m)-fold Darboux transformation, which admits m spectral parameters, are proposed based on that N-fold Darboux transformation, where m is a positive integer. One-, two- and three-soliton solutions of that system are determined via that N-fold Darboux transformation. Double-pole and triple-pole soliton solutions of that system are derived via that (1, N − 1)-fold Darboux transformation. Those solitons are graph- ically represented for the magnetization and external magnetic field related to a ferrite.

show abstract

“…Exact solutions of such physical meaningful nonlinear partial differential equations (NPDEs) are very important in practical applications. The exact solutions of these NPDEs generally employ a variety of analytical methods such as inverse scattering transform [1,2], Darboux transformation [3][4][5], Hirota method [6,7], Bäcklund transformation [8][9][10], etc. In this paper, we will use the method which uses conservation laws to construct high-dimensional integrable systems.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal symmetries and solutions of the multi-dimensional integrable long water wave equations

Jin,

Yang,

Xin

2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, the (2+1)-dimensional integrable long water wave equations (LWWs) are constructed for the first time using the conservation law of the (1+1)-dimensional LWWs. The new (1+1)-dimensional LWWs can be obtained by introducing a constraint to the (2+1)-dimensional LWWs. This new (1+1)-dimensional LWWs are studied by using nonlocal symmetry methods for the first time. The closed system corresponding to nonlocal symmetry is established by the lax pairs of equations and the potential function determined using conservation laws. Exact solutions of the equations are obtained by finite symmetrytransformation and symmetry approximation of this closed system. The dynamic behavior of the equations is studied by means of figures of the exact solutions.

show abstract

N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material

Cited by 91 publications

References 63 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

Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformations and solitons

Nonlocal symmetries and solutions of the multi-dimensional integrable long water wave equations

Contact Info

Product

Resources

About