☆ 4.5 Article

Rational and Semi-Rational Solutions to the (2

AXIOMS (2022)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Mathematics, Applied

Analysis and profiles of travelling wave solutions to a Darcy-Forchheimer fluid formulated with a non-linear diffusion

S. Rahman et al.

Summary: The intention of this study is to explore the existence, uniqueness, regularity of solutions, and profiles of travelling waves in a Darcy-Forchheimer fluid flow with nonlinear diffusion. The formulation of such flow is a novel aspect of this study and requires appropriate mathematical treatment to handle the introduced degenerate diffusivity. Firstly, the existence, regularity, and uniqueness are analyzed using an appropriate test function. Then, the problem is formulated in the travelling wave domain and analyzed near critical points using the Geometric Perturbation Theory. Based on this theory, precise and asymptotic profiles of travelling waves are obtained. Additionally, the Geometric Perturbation Theory is used to provide evidence of the normal hyperbolicity in the involved manifolds that are used to obtain the associated travelling wave solutions. The main finding, which is non-trivial in the case of nonlinear diffusion, is the existence of an exponential profile along the travelling frame. Lastly, a numerical exercise is conducted to validate the obtained analytical solutions.

AIMS MATHEMATICS (2022)

添加到收藏夹

Article Mathematics, Applied

Rogue waves in (2+1)-dimensional three-wave resonant interactions

Bo Yang et al.

Summary: Rogue waves in (2+1)-dimensional three-wave resonant interactions were studied using the bilinear KP reduction method. Different types of rogue waves were derived from constant, lump-soliton, and dark-soliton backgrounds, each exhibiting unique patterns and dynamics. Rogue waves originating from dark-soliton backgrounds featured novel intensity patterns such as half-line shapes or lump shapes.

PHYSICA D-NONLINEAR PHENOMENA (2022)

添加到收藏夹

Article Mathematics, Applied

Traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey

Yujuan Jiao et al.

Summary: This paper investigates the traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey. Firstly, the existence and non-existence of weak traveling wave solutions are proved using the upper and lower solutions method. Furthermore, it is proven that the weak traveling wave solutions are actually traveling wave solutions under additional conditions by using Lyapunov function method and LaSalle's invariance principle.

AIMS MATHEMATICS (2022)

添加到收藏夹

Article Mathematics, Applied

Analysis of travelling wave solutions for Eyring-Powell fluid formulated with a degenerate diffusivity and a Darcy-Forchheimer law

Jose Luis Diaz Palencia et al.

Summary: This paper provides analytical assessments for a fluid flowing in a porous medium with a non-linear diffusion and a degenerate diffusivity. Regularity, existence, and uniqueness of solutions are analyzed, and traveling wave solutions are studied. The exponential decaying rate in the traveling wave profile is validated through numerical assessment.

AIMS MATHEMATICS (2022)

添加到收藏夹

Article Mathematics, Applied

New rational and breather solutions of a higher-order integrable nonlinear Schrodinger equation

Li-Yuan Ma et al.

Summary: This letter investigates the general rational solutions and breather solutions of a higher-order integrable nonlinear Schrodinger equation based on Darboux transformation. New W-shape traveling wave solution, rogue wave solution, and various periodic breather solutions are constructed. The interaction properties of two breather solutions are displayed through numerical simulation, showing new dynamical properties in extended nonlinear integrable physical models.

APPLIED MATHEMATICS LETTERS (2021)

添加到收藏夹

Article Mathematics, Applied

Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation

Run-Fa Zhang et al.

Summary: This paper investigates the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like (CDGKS-like) equation and constructs generalized lump solutions, classical lump solutions and novel solutions using neural network methods. The results fill a gap in the existing literature on the CDGKS-like equation and showcase the dynamical characteristics of these waves through various plots. The effective methods employed in this study are beneficial for studying nonlinear evolution equations in plasmas, mathematical physics, electromagnetism, and fluid dynamics.

APPLIED MATHEMATICS AND COMPUTATION (2021)

添加到收藏夹

Article Mathematics, Applied

A new set and new relations of multiple soliton solutions of (2+1)-dimensional Sawada-Kotera equation

Ruoxia Yao et al.

Summary: A new transformation is reported to formulate multiple soliton solutions of the 2DSK equation and establish a unique relationship between these solutions. This study also shows a connection between two equations.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

添加到收藏夹

Article Physics, Multidisciplinary

Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions

Weifang Weng et al.

Summary: Based on the matrix Riemann-Hilbert problem, the inverse scattering transform for the focusing nonlinear Schrodinger equation with triple zeros of scattering coefficients is presented. General N-triple-pole solutions for the potential and explicit expressions for the reflectionless potential are found, along with trace formulae and theta conditions. The obtained triple-pole solutions are useful for explaining related nonlinear wave phenomena.

PHYSICS LETTERS A (2021)

添加到收藏夹

Article Physics, Multidisciplinary

Travelling waves and instability in a Fisher-KPP problem with a nonlinear advection and a high-order diffusion

Jose Luis Diaz Palencia

Summary: This paper examines the instability of travelling waves in high-order differential operators, focusing on the characterization of TW instability, TW propagation speed, and positive monotone behavior of solutions in a local inner region. The authors provide a sharp estimation of the TW propagation speed to ensure the existence of a positive inner region, as well as insights on regularity, existence, and uniqueness of solutions.

EUROPEAN PHYSICAL JOURNAL PLUS (2021)

添加到收藏夹

Article Chemistry, Multidisciplinary

Travelling Waves Approach in a Parabolic Coupled System for Modelling the Behaviour of Substances in a Fuel Tank

Jose Luis Diaz Palencia

Summary: This study aimed to provide a formulation of a non-linear diffusion model with forced convection in the form of a reaction-absorption system. The model was studied using analytical and numerical approaches within the framework of the parabolic operators theory. The solutions were applied to study a gas interaction phenomenon in order to ensure the safety of an aircraft fuel tank by creating an inerted ullage. The study used the travelling wave solutions approach to investigate the existence and stability of solutions.

APPLIED SCIENCES-BASEL (2021)

添加到收藏夹

Article Mathematics

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

Wen-Xiu Ma et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2018)

添加到收藏夹

Article Mathematics, Applied

The Derivative Yajima-Oikawa System: Bright, Dark Soliton and Breather Solutions

Junchao Chen et al.

STUDIES IN APPLIED MATHEMATICS (2018)

添加到收藏夹

Article Mathematics, Applied

Rogue wave and a pair of resonance stripe solitons to KP equation

Xiaoen Zhang et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2018)

添加到收藏夹

Article Engineering, Mechanical

Deformation rogue wave to the (2+1)-dimensional KdV equation

Xiaoen Zhang et al.

NONLINEAR DYNAMICS (2017)

添加到收藏夹

Article Engineering, Mechanical

Solving the -dimensional KP-Boussinesq and BKP-Boussinesq equations by the simplified Hirota's method

Abdul-Majid Wazwaz et al.

NONLINEAR DYNAMICS (2017)

添加到收藏夹

Article Mathematics, Applied

Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation

Xiaoen Zhang et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2017)

添加到收藏夹

Article Mathematics, Applied

Rational solutions and lump solutions to the generalized (3+1)-dimensional Shallow Water-like equation

Yong Zhang et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2017)

添加到收藏夹

Article Physics, Multidisciplinary

General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System

Junchao Chen et al.

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN (2015)

添加到收藏夹

Article Physics, Mathematical

The rogue wave and breather solution of the Gerdjikov-Ivanov equation

Shuwei Xu et al.

JOURNAL OF MATHEMATICAL PHYSICS (2012)

添加到收藏夹

Article Physics, Fluids & Plasmas

Observation of a hierarchy of up to fifth-order rogue waves in a water tank

A. Chabchoub et al.

PHYSICAL REVIEW E (2012)

添加到收藏夹

Article Multidisciplinary Sciences

General high-order rogue waves and their dynamics in the nonlinear Schrodinger equation

Yasuhiro Ohta et al.

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2012)

添加到收藏夹

Article Physics, Multidisciplinary

The Peregrine soliton in nonlinear fibre optics

B. Kibler et al.

NATURE PHYSICS (2010)

添加到收藏夹

Article Physics, Fluids & Plasmas

Rogue waves and rational solutions of the Hirota equation

Adrian Ankiewicz et al.

PHYSICAL REVIEW E (2010)

添加到收藏夹

Article Physics, Multidisciplinary

Waves that appear from nowhere and disappear without a trace

N. Akhmediev et al.

PHYSICS LETTERS A (2009)

添加到收藏夹

Article Physics, Multidisciplinary

Coalescence of ripplons, breathers, dromions and dark solitons

DWC Lai et al.

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN (2001)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.