Rogue-wave, rational and semi-rational solutions for a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer fluid

Liu, Fei-Yan; Gao, Yi–Tian; Yu, Xin

doi:10.1007/s11071-022-08017-x

Cited by 26 publications

(4 citation statements)

References 63 publications

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“…( ) ˆ( ), a variable-coefficient generalized Korteweg-de Vries model with dissipative, perturbed and external-force terms for the pulse waves in a blood vessel or dynamics in a circulatory system [17] (and references therein) r r h r h By the bye, more nonlinear evolution equations might be found, for instance, in [24][25][26][27][28].…”

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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“…It is pointed out that rogue wave solutions can also be generated by positive polynomial solutions [28]. This was followed by other researchers to solve first order and muti-order rogue waves by using symbolic computation method [29][30][31][32][33][34][35][36][37]. A number of research results show that with the development of symbolic computation and data processing technology, symbolic computation with test function is a powerful method to study the interaction phenomenon [38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

Cao,

Yin,

et al. 2024

Phys. Scr.

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In this study, two new theorems are generalized. We obtained a new paradigm about the second order rogue wave and multiple exponential functions, and a new paradigm about the second order rogue wave and multiple hyperbolic cosine functions. Six sets of interaction solutions of the model are solved by means of symbolic calculation and two new theorems. Meaningful graphs of the propagation processes along time demonstrated the interaction phenomena for these solutions. The energy transfer process can be observed when the second order rogue waves interact with multiple exponential functions or multiple hyperbolic cosine functions. As a conclusion from our paper, the solitons’ energy transfers to the second order rogue wave at beginning, the rogue wave’s energy dissipates and transfers to the solitons along the time moving. It will contribute to the research on the generation of rogue waves.

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“…Up to now, some well-developed methods have been put forward to derive the localized waves of NLEEs, including the Hirota's bilinear method [9,13,14], Kadomtsev-Petiashvili hierarchy reduction [15], the Darboux transformation [16,17], Bäcklund transformation [18], Lie group method [19], Pfaffian technique [20], long wave limit method [21][22][23], velocity resonance method [24,25], bilinear neural network method [26], ¶-dressing method [27] and so on. Based on these methods, a variety of localized wave solutions with different lump soliton [28], rogue wave.…”

Section: Introductionmentioning

confidence: 99%

“…c) depicts the spatial structure and projection on (x,y)-plane. Actually, the lump wave for equation (1) is generated from u x y z t f has been defined in(15) with N = 2M,…”

mentioning

confidence: 99%

The excitation of high-order localized waves in (3+1)-dimensional Kudryashov-Sinelshchikov equation

Li,

Cheng,

Dai

2024

Phys. Scr.

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The aim of this work is to explore the excitation of high-order localized waves in the (3+1)-dimensional Kudryashov-Sinelshchikov equation, which is used to describe the dynamic of liquid with gas bubble. First of all, classical N-soliton solutions are constructed by means of Hirota bilinear form and symbolic calculation. What’s more, the high-order breather waves are derived through the degeneration process of the N-soliton solutions with conjugate parameter. Then, high-order lump waves are constructed by taking long wave limit technique on N-soliton solutions. Finally, the high-order mixed localized waves involving resonant Y-type solitons, high-order breather waves and high-order lump waves are obtained by utilizing some comprehensive methods. Abundant dynamical and evolutionary behaviors of these results are investigated specifically, some figures are presented to shed light on the nonlinear phenomena hidden in the high-order localized waves vividly.

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Rogue-wave, rational and semi-rational solutions for a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer fluid

Cited by 26 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

Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

The excitation of high-order localized waves in (3+1)-dimensional Kudryashov-Sinelshchikov equation

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