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Symmetry
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Nonlinear Dynamics and Applied Partial Differential Equations
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Nonlinear Dynamics and Applied Partial Differential Equations

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 3334

Special Issue Editors

Prof. Dr. Vallampati Ramachandra Prasad

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Guest Editor
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
Interests: heat transfer; fluid dynamics
Dr. Venkatadri Kothuru

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Guest Editor
Department of Mathematics, Indian Institute of Information Technology Sri City, Andhra Pradesh, India
Interests: computational fluid dynamics
Dr. Sivaraj Ramachandran

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Guest Editor
Department of Mathematics, Dr B R Ambedkar National Institute of Technology Jalandhar, Punjab 144011, India
Interests: heat and mass transfer studies on viscoelastic fluid flows

Special Issue Information

Dear Colleagues,

Nonlinear partial differential equations arise in a wide variety of physical problems and areas such as engineering dynamics, fluid dynamics, plasma physics, solid mechanics and quantum field theory.

This Special Issue invites researchers belonging to a wide variety of fields to contribute high-quality and original research articles, as well as review articles. Topics should include discussions of nonlinear dynamics and the analysis of nonlinear partial differential equations. Specifically, submissions should discuss Navier–Stokes–Poisson equations, reaction–diffusion equations, nonlinear pseudo parabolic and hyperbolic equations, Newtonian and non-Newtonian fluid equations, magneto-hydrodynamic equations, nonlinear heat equations,  Navier–Stokes equations, Boussinesq approximations equations, biological fluid dynamics, symmetric and axisymmetric flows, theory of partial differential equations, and numerical methods of partial differential equations.

Prof. Dr. Vallampati Ramachandra Prasad
Dr. Venkatadri Kothuru
Dr. Sivaraj Ramachandran
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear dynamics 
  • nonlinear partial differential equations 
  • mathematical modelling of partial differential equations in enginnering and applied sciences 
  • numerical methods in partial differential equations

Published Papers (3 papers)

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Research

12 pages, 3008 KiB  
Article
Wobbling Fractals for The Double Sine–Gordon Equation
by Attilio Maccari
Symmetry 2023, 15(3), 639; https://doi.org/10.3390/sym15030639 - 03 Mar 2023
Viewed by 822
Abstract
This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution. In the case λ = 0, we get [...] Read more.
This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution. In the case λ = 0, we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ = −1/8, we derive a phase-locked solution with the same frequency of the linear case. In general, we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. Using symmetry considerations, we can demonstrate the existence of envelope wobbling solitary waves, due to the critical observation the phase modulation depending on the solution amplitude and on the position. Because the double sine–Gordon equation has a very rich behavior, including wobbling chaotic and fractal solutions due to an arbitrary function in its solution, the main conclusion is that it is too reductive to focus only on coherent solutions. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Applied Partial Differential Equations)
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10 pages, 3200 KiB  
Article
Rogue Waves Generator and Chaotic and Fractal Behavior of the Maccari System with a Resonant Parametric Forcing
by Attilio Maccari
Symmetry 2022, 14(11), 2321; https://doi.org/10.3390/sym14112321 - 04 Nov 2022
Cited by 1 | Viewed by 1034
Abstract
Using the Asymptotic Perturbation (AP) method we can find approximate solutions for the Maccari equation with a parametric resonant forcing acting over the frequency of a generic mode. Taking into account its nonlocal behavior and applying symmetry considerations, a system with two coupled [...] Read more.
Using the Asymptotic Perturbation (AP) method we can find approximate solutions for the Maccari equation with a parametric resonant forcing acting over the frequency of a generic mode. Taking into account its nonlocal behavior and applying symmetry considerations, a system with two coupled equations for the phase and amplitude modulation can be obtained. The system can be solved, and we demonstrate the existence of a big modulation in the wave amplitude, producing a rogue waves train and, in this case, these waves are not isolated. We then obtain a rogue waves generator, being able of producing and controlling the rogue waves’ amplitude. Another important finding is the existence of chaotic or fractal solutions, because of the presence of an arbitrary function in the solution. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Applied Partial Differential Equations)
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8 pages, 1396 KiB  
Article
A Parametric Resonance for the Nonlocal Hirota–Maccari Equation
by Attilio Maccari
Symmetry 2022, 14(7), 1444; https://doi.org/10.3390/sym14071444 - 14 Jul 2022
Cited by 3 | Viewed by 1018
Abstract
The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an [...] Read more.
The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an infinite-period bifurcation when the parametric force increases its value. Moreover, symmetry considerations suggest performing a global analysis of the two couples, in such a way that we find an energy-like function and corroborate and verify the existence of this infinite period bifurcation. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Applied Partial Differential Equations)
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