Darboux transformation, localized waves and conservation laws for an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.svg"><mml:mi>M</mml:mi></mml:math>-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber

Yang, Dan-Yu; Tian, Bo; Tian, Huiping; Wei, Cheng-Cheng; Shan, Wen-Rui; Jiang, Yan

doi:10.1016/j.chaos.2021.111719

Cited by 61 publications

(9 citation statements)

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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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“…Subsequently, we can rewrite equation (1) as the sum of some terms of F (0) , F¢, F″, F‴, F (4) , F (5) , F (6) and F (7) based on expressions (4), ( 5) and (6). Then setting their coefficients to zero:…”

Section: = ¢ +mentioning

confidence: 99%

“…And a large number of solutions of NLEEs with different forms such as rogue wave and lump wave solutions [4] are studied. Some methods have been proposed by scientists to study analytic solutions of NLEEs, such as Darboux transformation [5,6], the Hirota bilinear method [7][8][9][10], the inverse scattering method [11], Bäcklund transformation [12,13], exp-function method [14,15]and other methods [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

Ma,

Su,

Deng

2023

Phys. Scr.

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In this paper, the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation is an object of the research. Based on the extended homogeneous balancing method, Auto-B$\rm{\ddot a}$cklund transformations are obtained in two cases. Subsequently, with the help of these transformations, we obtain various explicit solutions of this equation. We attain complexiton solutions consisting of exponential, hyperbolic and trigonometric solutions from the Hirota bilinear form of this equation through the extended transformed rational function method. Also, we derive one-kink and two-kink soliton solutions by Maple symbolic calculation and the breather-wave solution via the extended homoclinic test approach. In addition, 3D graphics and density plots of the obtained solutions are depicted to illustrate the dynamical features of these solutions

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“…Fluid mechanics has been regarded as the study of the fundamental mechanisms and force of liquids, plasmas and gases, with applications in astrophysics, meteorology, oceanography and biomedical engineering [1][2][3][4]. Methods have been introduced to solve the nonlinear evolution equations, including the Bäcklund transformation, Darboux transformation and the Lie symmetry approach [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

Liu

Gao

2023

Commun. Theor. Phys.

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Under investigation in this paper is a (2+1)-dimensional variable-coefficient modified dispersive water-wave (vcMDWW) system in fluid mechanics. We prove the Painlevé integrability for the vcMDWW system via the Painlevé analysis. We get auto-Bäcklund transformations for the vcMDWW system via the truncated Painlevé expansions. Bilinear forms and N-soliton solutions are constructed, where N is a positive integer. We discuss the inelastic, elastic interactions and soliton resonances for the two solitons. We graphically demonstrate that velocities of the solitons are affected by the variable coefficient of that system.

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Darboux transformation, localized waves and conservation laws for an M-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber

Cited by 61 publications

References 50 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

Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

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