☆ 4.6 Article

The solitary wave, kink and anti-kink solutions coexist at the same speed in a perturbed nonlinear Schrodinger equation

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2023)

Related references

Note: Only part of the references are listed.

Article Mathematics, Applied

Traveling waves in a generalized Camassa-Holm equation involving dual-power law nonlinearities

Huimin Qiu et al.

Summary: This article focuses on the properties and persistence of traveling waves including peakons, periodic peakons, compactons, and solitary waves in a generalized Camassa-Holm (gCH) equation. The global phase portraits of the traveling wave system are analyzed using a dynamical system-based approach, leading to the classification of these waves and the determination of their corresponding parameter conditions. The existence of solitary waves in a perturbed gCH equation is investigated using geometric singular perturbation theory (GSPT) and an explicit Melnikov method. The article also presents a method for calculating the unperturbed homoclinic orbits and the associated Melnikov integral in an explicit way.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2022)

Add to Collection

Article Mathematics, Applied

Monotonicity of limit wave speed of traveling wave solutions for a perturbed generalized KdV equation

Aiyong Chen et al.

Summary: This study examines traveling wave solutions of a perturbed generalized KdV equation and proves that the limit wave speed is decreasing by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are provided, partially addressing an open question previously proposed by Yan et al. (2014).

APPLIED MATHEMATICS LETTERS (2021)

Add to Collection

Article Mathematics

Traveling pulse solutions of a generalized Keller-Segel system with small cell diffusion via a geometric approach

Zengji Du et al.

Summary: This paper investigates the existence of traveling pulse solutions in one-dimensional generalized Keller-Segel system by using the dynamical systems approach, specifically based on geometric singular perturbation theory and Poincare-Bendixson theorem. The dynamics of the system is analyzed using geometric singular perturbation theory, an invariant region for the associated traveling wave equation is sought, and then Poincare-Bendixson theorem is applied to show the existence of traveling pulse solutions. The main results are illustrated with two examples presented as applications.

JOURNAL OF DIFFERENTIAL EQUATIONS (2021)

Add to Collection

Article Engineering, Mechanical

New type of solitary wave solution with coexisting crest and trough for a perturbed wave equation

Lijun Zhang et al.

Summary: In this paper, the perturbed mK(3,1) equation was restudied using the geometric singular perturbation theorem and bifurcation analysis to explore the dynamics of solitary wave solutions. It was found that the equation has a new family of solitary waves that decay to constants determined by wave speeds and a parameter, as well as a new type of solitary waves with coexisting crest and trough. The theoretical results were confirmed through numerical simulations.

NONLINEAR DYNAMICS (2021)

Add to Collection

Article Mathematics, Applied

Dynamics of the predator-prey model with the Sigmoid functional response

Xianfeng Chen et al.

Summary: This study investigates the global stability and characteristics of limit cycles in the predator-prey model with a Sigmoid functional response. It is found that when the positive equilibrium is a weak focus, it is a stable weak focus of order 1, and various types of limit cycles may exist, including canard cycles and relaxation oscillations.

STUDIES IN APPLIED MATHEMATICS (2021)

Add to Collection

Article Mathematics, Applied

Coexistence of the solitary and periodic waves in convecting shallow water fluid

Xianbo Sun et al.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2020)

Add to Collection

Article Mathematics, Interdisciplinary Applications

A New Type of Solitary Wave Solution of the mKdV Equation Under Singular Perturbations

Lijun Zhang et al.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2020)

Add to Collection

Article Mathematics

The dynamics of traveling waves for a nonlinear Belousov-Zhabotinskii system ?

Zengji Du et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2020)

Add to Collection

Article Mathematics, Applied

EXISTENCE OF PERIODIC WAVES FOR A PERTURBED QUINTIC BBM EQUATION

Lina Guo et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2020)

Add to Collection

Article Engineering, Mechanical

New solitary wave solutions in a perturbed generalized BBM equation

Kun Zhu et al.

NONLINEAR DYNAMICS (2019)

Add to Collection

Article Mathematics

Canards, heteroclinic and homoclinic orbits for a slow-fast predator-prey model of generalized Holling type III

Cheng Wang et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2019)

Add to Collection

Article Optics

Grey and black optical solitary waves, and modulation instability analysis to the perturbed nonlinear Schrodinger equation with Kerr law nonlinearity

Mustafa Inc et al.

JOURNAL OF MODERN OPTICS (2019)

Add to Collection

Article Mathematics, Applied

Existence of Kink Waves and Periodic Waves for a Perturbed Defocusing mKdV Equation

Aiyong Chen et al.

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS (2018)

Add to Collection

Article Mathematics

The existence of solitary wave solutions of delayed Camassa-Holm equation via a geometric approach

Zengji Du et al.

JOURNAL OF FUNCTIONAL ANALYSIS (2018)

Add to Collection

Article Mathematics, Applied

ON KINK AND ANTI-KINK WAVE SOLUTIONS OF SCHRODINGER EQUATION WITH DISTRIBUTED DELAY

Chuanhai Xu et al.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION (2018)

Add to Collection

Article Mathematics, Applied

Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrodinger-type equations

E. M. E. Zayed et al.

APPLIED MATHEMATICS AND COMPUTATION (2016)

Add to Collection

Article Mathematics

Existence of solitary waves and periodic waves for a perturbed generalized BBM equation

Aiyong Chen et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2016)

Add to Collection

Article Mathematics, Applied

BIFURCATIONS OF EXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED R-K-L EQUATION

Jianming Zhang et al.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION (2016)

Add to Collection

Article Mathematics

Geometric singular perturbation theory with real noise

Ji Li et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2015)

Add to Collection

Article Mathematics, Applied

INVARIANT FOLIATIONS FOR RANDOM DYNAMICAL SYSTEMS

Ji Li et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2014)

Add to Collection

Article Mathematics

Existence of Solitary Waves and Periodic Waves to a Perturbed Generalized KdV Equation

Weifang Yan et al.

MATHEMATICAL MODELLING AND ANALYSIS (2014)

Add to Collection

Article Mathematics, Applied

A geometric construction of traveling waves in a generalized nonlinear dispersive-dissipative equation

M. B. A. Mansour

JOURNAL OF GEOMETRY AND PHYSICS (2013)

Add to Collection

Article Mathematics

NORMALLY HYPERBOLIC INVARIANT MANIFOLDS FOR RANDOM DYNAMICAL SYSTEMS: PART I - PERSISTENCE

Ji Li et al.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2013)

Add to Collection

Article Mathematics, Applied

Exact solutions of a two-dimensional nonlinear Schrodinger equation

Aly R. Seadawy

APPLIED MATHEMATICS LETTERS (2012)

Add to Collection

Article Engineering, Multidisciplinary

Traveling wave solutions for Schrodinger equation with distributed delay

Zhihong Zhao et al.

APPLIED MATHEMATICAL MODELLING (2011)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Exact analytic solitary wave solutions for the RKL model

Houria Triki et al.

MATHEMATICS AND COMPUTERS IN SIMULATION (2009)

Add to Collection

Article Physics, Multidisciplinary

1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation

Anjan Biswas

PHYSICS LETTERS A (2009)

Add to Collection

Article Optics

Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schrodinger equations

M. Vijayajayanthi et al.

PHYSICAL REVIEW A (2008)

Add to Collection

Article Mathematics, Applied

Travelling waves for the population genetics model with delay

Guojian Lin et al.

ANZIAM JOURNAL (2006)

Add to Collection

Article Mathematics, Applied

Stability and evolution of solitary waves in perturbed generalized nonlinear Schrodinger equations

JK Yang et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2000)

Add to Collection

© Peeref 2019-2024. All rights reserved.