Title Prof. First Name ARVIND Last Name PATEL
Designation Professor
Department Department of Mathematics
Email apatel@maths.du.ac.in
Webpage
Phone.no 011-27666658
Employement Info
Employee Type Nature Of Employment
Teaching Permanent
Educational Qualifications
Degree/Certification Name Institution Year of Completion
Ph.D. - PhD DDU Gorakhpur University Gorakhpur 2009
PG DDU Gorakhpur University Gorakhpur 2000
UG DDU Gorakhpur University Gorakhpur 1998
HSC Board of High School and Intermediate Education, Uttar Pradesh 1995
SSC Board of High School and Intermediate Education, Uttar Pradesh 1993
Qualifications
Examination Name Conducting Body Date of Passing
NET CSIR, New Delhi 26-06-2003
Fellowship Details
Name Of Fellowship Awarding Body Fellowship Level
Junior Research Felloship CSIR National
Senior Research Fellowship CSIR, New Delhi National
Teaching Experience (Within Institution)
Designation Duration
Guest Lecturer 01-07-2003 To 13-03-2007 (3 years, 8 months, 12 days)
Lecturer 14-03-2007 To 29-10-2009 (2 years, 7 months, 15 days)
Assistant Professor 30-10-2009 To 13-03-2019 (9 years, 4 months, 11 days)
Associate Professor 14-03-2019 To 13-03-2021 (1 years, 11 months, 27 days)
Professor 14-03-2022 To 04-09-2022 (5 months, 21 days)
Administrative Experience (Within Institution)
Designation Duration
Associate Professor 01-07-2019 To 30-06-2020 (11 months, 29 days)
Associate Professor 01-07-2020 To 30-06-2021 (11 months, 29 days)
Associate Professor 01-07-2021 To 30-06-2022 (11 months, 29 days)
Professor 01-07-2023 To 06-10-2023 (3 months, 5 days)
Professor 01-07-2022 To 30-06-2023 (11 months, 29 days)
Courses/Subjects Taught
Teaching Activity Type Course Title Semester Total Assigned Classes Number of Classes Taught Duration
Lecture Complex Analysis 1 60 57 03-12-2021 To 21-03-2022 (3 months, 18 days)
Research Supervision Overview
PhD Scholars Supervised PhD Degrees Awarded Theses Submitted
4 6 0
M.Phil Scholars Supervised M.Phil Degrees Awarded M.Phil Theses Submitted
1 15 0
Research Publications
Title of Article Type of Publication Name of Journal ISSN Journal Volume Year Link to Article DOI (Digital Object Identifier)
Dynamical behaviour of soliton solutions and modulation instability analysis for a cold bosonic atoms in zig-zag optical lattice model Research Papers in Web of Science Listed Journals Pramana 99 2025 https://link.springer.com/article/10.1007/s12043-025-03016-0 https://doi.org/10.1007/s12043-025-03016-0
Heat and Mass Transfer Under MHD Mixed Convection in an Adjacent Two‐Sided Lid‐Driven Square Cavity Research Papers in Scopus Listed Journals Heat Transfer 2025 https://onlinelibrary.wiley.com/doi/10.1002/htj.22993 https://doi.org/10.1002/htj.70120
Dynamics of solitons and modulation instability in a (2+1)-dimensional coupled nonlinear Schrdinger equation Research Papers in Web of Science Listed Journals Mathematics and Computers in Simulation ISSN: 1872-7166 235 2025 https://www.sciencedirect.com/science/article/pii/S0378475425000965 https://doi.org/10.1016/j.matcom.2025.03.022
Shock wave structure in carbon dioxide using one and multi-temperature model Research Papers in Web of Science Listed Journals Indian Journal of Physics eISSN 0974-9845 2025 https://link.springer.com/journal/12648/articles https://doi.org/10.1007/s12648-024-03539-z
Lie group of similarity analysis of shock waves in viscous flow under magnetic field Research Papers in Web of Science Listed Journals Chinese Journal of Physics Online ISSN: 2309-9097 92 2024 https://www.sciencedirect.com/science/article/pii/S057790732400443X https://doi.org/10.1016/j.cjph.2024.11.014
Self-similar flow behind a shock wave in a gas under the effect of viscosity, heat conduction, and variable ambient density Research Papers in Web of Science Listed Journals Physica Scripta 1402-4896 99 2024 https://iopscience.iop.org/article/10.1088/1402-4896/ad6f4f DOI 10.1088/1402-4896/ad6f4f
Heat and mass transfer under MHD mixed convection in a four-sided lid-driven square cavity Research Papers in Scopus Listed Journals Heat Transfer 2688-4542 2024 https://onlinelibrary.wiley.com/doi/full/10.1002/htj.22993 doi:10.100 2/htj.22993
Dynamical behaviour of solitons and modulation instability analysis of a nonautonomous (1 + 1)-dimensional nonlinear Schrödinger equation Research Papers in Web of Science Listed Journals Optik : International Journal for Light and Electron Optics ISSN: 1618-1336 293 https://doi.org/10.1016/j.ijleo.2023.171412
Shock wave structure in non-polar diatomic and poly-atomic dense gases under rotation and vibration Research Papers in Web of Science Listed Journals Physics of Fluids 10706631 34 https://aip.scitation.org/doi/10.1063/5.0097397 https://doi.org/10.1063/5.0097397
Heat and mass transfer in a two-sided lid-driven square cavity with non-uniform sinusoidal heating on horizontal walls Research Papers in Web of Science Listed Journals The European Physical Journal Plus 2190-5444 134 https://link.springer.com/article/10.1140/epjp/s13360-021-02040-4 https://doi.org/10.1140/epjp/s13360-021-02040-4
Mixed convection in a two-sided and four-sided lid-driven square porous cavity Research Papers in Web of Science Listed Journals International Journal of Heat and Technology 0392-8764 39(3) https://www.iieta.org/journals/ijht/paper/10.18280/ijht.390305 https://doi.org/10.18280/ijht.390305
Modulation instability analysis of a nonautonomous (3+1)-dimensional coupled nonlinear Schrödinger equation Research Papers in Web of Science Listed Journals Non-linear Dynamics 1573-269X 104 https://link.springer.com/article/10.1007/s11071-021-06558-1 https://doi.org/10.1007/s11071-021-06558-1
Dispersion and phase managed optical soliton solutions of a nonautonomous (3+1)-dimensional coupled nonlinear Research Papers in Web of Science Listed Journals OPTIK 0030-4026 242 https://www.sciencedirect.com/science/article/pii/S0030402621003673?via%3Dihub https://doi.org/10.1016/j.ijleo.2021.166648
Similarity Solution for the Flow Behind a Magnetogasdynamic Exponential Shock Wave in a Perfect Gas with Varying Density, Heat Conduction, and Radiation Heat Flux Research Papers in Web of Science Listed Journals Journal of Engineering Physics and Thermophysics 1062-0125 94(1) https://link.springer.com/article/10.1007/s10891-021-02288-8 https://doi.org/10.1007/s10891-021-02288-8
Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation Research Papers in Web of Science Listed Journals SN Applied Sciences 2523-3971 2 https://link.springer.com/article/10.1007/s42452-020-03815-7 https://doi.org/10.1007/s42452-020-03815-7
Shock wave structure in non-ideal dilute gas under variable Prandtl number Research Papers in Web of Science Listed Journals Shock Waves 0938-1287 30(6) https://link.springer.com/article/10.1007/s00193-020-00972-x DOI 10.1007/s00193-020-00972-x
Construction of the soliton solutions and modulation instability analysis for the Mel'nikov system Research Papers in Web of Science Listed Journals Chaos, Solitons and Fractals 0960-0779 140 https://www.sciencedirect.com/science/article/pii/S0960077920305555?via%3Dihub https://doi.org/10.1016/j.chaos.2020.110159
The four-sided lid driven square cavity using stream function-vorticity formulation Research Papers in Web of Science Listed Journals Journal of Applied Mathematics and Computational Mechanics 2353-0588 19(2) https://amcm.pcz.pl/?id=view&volume=19&issue=2&article=2 DOI: 10.17512/jamcm.2020.2.02
Travelling wave solution of a Riemann problem and shock structure in an unsteady flow of a perfect gas under viscosity Research Papers in Web of Science Listed Journals International Journal of Heat and Technology 0392-8764 37(3) https://www.iieta.org/journals/ijht/paper/10.18280/ijht.370329 https://doi.org/10.18280/ijht.370329

Shock wave structure in a non-ideal gas under temperature and density dependent viscosity and heat conduction Research Papers in Web of Science Listed Journals Theoretical and Computational Fluid Dynamics 0935-4964 33 https://doi.org/10.1007/s00162-019-00505-y DOI 10.1007/s00162-019-00505-y
Soliton solutions and modulation instability analysis of the coupled Zakharov-Kuznetsov equation Research Papers in Web of Science Listed Journals European Physical Journal Plus 2190-5444 134 https://link.springer.com/article/10.1140/epjp/i2019-12521-6 DOI 10.1140/epjp/i2019-12521-6
Exact solution of shock-wave structure in a non-ideal gas under constant and variable coefficient Research Papers in Web of Science Listed Journals Shock Waves 0938-1287 29 https://link.springer.com/article/10.1007/s00193-018-0855-8 https://doi.org/10.1007/s00193-018-0855-8
Study of generalized ZK-BBM equation to construct solitary patterns solutions via variational iteration method Research Papers in Peer Reviewed Journals Far East Journal of Mathematical Sciences 0972-0871 103(11) http://www.pphmj.com/abstract/11652.htm http://dx.doi.org/10.17654/MS103111721
Self similar flow behind an exponential shock wave in a self-gravitating, rotating axisymmetric dusty gas with heat conduction and radiation heat flux Research Papers in Web of Science Listed Journals Indian Journal of Physics 0973-1458 92(9) https://link.springer.com/article/10.1007/s12648-018-1199-z https://doi.org/10.1007/s12648-018-1199-z
Travelling wave solution of shock structure in an unsteady flow of a viscous non-ideal gas Research Papers in UGC listed Journals Ganita 0046-5402 68(1) http://bharataganitaparisad.com/ganita-volume-68-1/ No DOI
Dark and kink soliton solution of generalized ZKBBM equation by iterative scheme Research Papers in Web of Science Listed Journals Chinese Journal of Physics 0577-9073 56 https://www.sciencedirect.com/science/article/abs/pii/S0577907317313126?via%3Dihub https://doi.org/10.1016/j.cjph.2018.03.012
Homotopy analysis method for one dimensional unsteady adiabatic gas flow Research Papers in Scopus Listed Journals International Journal of Pure and Applied Mathematics 1311- 8080 115(4) https://ijpam.eu/contents/2017-115-4/3/index.html DOI: 10.12732/ijpam.v115i4.3
Similarity Solution for a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas with heat conduction and radiation heat flux Research Papers in Scopus Listed Journals Journal of Applied Fluid Mechanics 1735-3572 10(1) https://www.jafmonline.net/JournalArchive/article_432.html 10.18869/ACADPUB.JAFM.73.238.25679
Study of a one -dimensional unsteady gas dynamic problem by Adomian decomposition method Research Papers in Scopus Listed Journals International Journal of Applied Mathematics 1311-1728 29(6) http://www.diogenes.bg/ijam/contents/2016-29-6/8/index.html doi: http://dx.doi.org/10.12732/ijam.v29i6.8
A self-similar flow headed by a cylindrical shock wave in a rotating dusty gas Research Papers in Peer Reviewed Journals National Academy of Mathematics, India 0970-5228 28 No DOI
A self-similar Flow behind a Shock Wave in a Dusty Gas under a Gravitational Field Research Papers in Peer Reviewed Journals National Academy of Mathematics, India 0970-5228 27 No DOI
Self-similar solution of a shock propagation in a non-ideal gas Research Papers in Peer Reviewed Journals International Journal of Applied Mechanics and Engineering 1734- 4492 12(3) No DOI
Self-similar solution of Magnetogasdynamic spherical shock propagation in a rotating medium with radiation heat flux Research Papers in Peer Reviewed Journals South East Asian Journal of Mathematics and Mathematical Sciences 0972- 7752 5(2) No DOI
Research Projects
Project Title Project Type Year Of Sanction Outcome/Output Duration
Structure of shock waves in polyatomic gases, Minor 2021 Completed with one research paper published in Physics of Fluids 29-10-2021 To 15-03-2022 (4 months, 14 days)
Recent Analytic methods and their application in fluid flow problems Minor 2015 Completed with research publication 15-10-2015 To 14-10-2016 (11 months, 29 days)
Solution of system of hyperbolic conservation laws by Adomian Decomposition Methods and its application in fluid dynamics, Minor 2014 Completed with two research papers publication 15-10-2014 To 30-09-2015 (11 months, 15 days)
Shock Phenomena in Conducting and Non-Conducting Media Minor 2013 Completed with research insight in the topic 21-10-2013 To 15-03-2014 (4 months, 22 days)
Shock Phenomena in a dusty gas in absence and presence of magnetic field, heat conduction and thermal radiation Minor 2011 Completed with research insights 16-06-2011 To 15-02-2012 (7 months, 30 days)
Study of shock waves in gases under the effect of viscosity Minor 2023 Completed. One research paper published and one accepted for publication in SCIE Journals Ongoing since 31-08-2023 (2 years, 4 months, 13 days)
Structure of shock waves in two phase flow under the magnetic field Minor 2022 Three research papers are published in SCIE Journals. 31-08-2022 To 15-02-2023 (5 months, 15 days)
Shock waves in a viscous gas under the effect of heat conduction and magnetic field Minor 2024 Completed, Published three research papers, Two in SCIE and One in Scopus. Ongoing since 30-08-2024 (1 years, 4 months, 14 days)
Shock waves in a viscous gas under the effect of rotation and heat flux Minor 2025 Ongoing since 30-10-2025 (2 months, 14 days)
Professional Development Programmes
Programme Title Sponsoring Institution Organizing Institution Role Type of Programme
One week faculty development program on Communication and Presentation skill in Classroom teaching DUCC, University of Delhi, Delhi 110007 DUCC, University of Delhi, Delhi 110007 Attendee Faculty Development Programmes
Research Data Analysis using SPSS Delhi School of Analytics, IoE, Delhi University DUCC Delhi University and SPSS South Asia Attendee Other
Industrial Training on data Sciences and artificial Intelligence Delhi University, Delhi DUCC, Delhi University and DesignTech Systems Pvt. Ltd. Attendee Other
Webinar on Understanding Plagiarism Detection Software Ouriginal Delhi University, Delhi DUCC, University of Delhi in Association with e- Galactic Pune Attendee Faculty Development Programmes
Faculty Development Program on Cyber Security, High Performance Computing, AI/ML and GenAI Delhi University, Delhi DUCC University of Delhi and AWS Attendee Faculty Development Programmes
Refresher Course on Mathematical Sciences UGC New Delhi CPDHE- HRDC University of Delhi Attending Refresher Program
Instructional School for Lecturers in 'Numerical Analysis' National Centre for Mathematics Department of Mathematics, Panjab University, Chandigarh Attending Faculty Development Programmes
Conservation Laws with Applications to Continuum Mechanics National Centre for Mathematics Department of Mathematics, Panjab University, Chandigarh Attending Faculty Development Programmes
Workshop on MOOCs, e-content development and Open Educational Resources UGC-HRDC CPDHE (UGC-HRDC) University Of Delhi, Delhi Attending Short Term Program
Short term course on Research Methodology UGC-HRDC CPDHE (UGC-HRDC) University Of Delhi, Delhi Attending Short Term Program
Refresher course in Mathematical Sciences UGC CPDHE (UGC-HRDC)University Of Delhi Attending Refresher Program
ORE-81 UGC CPDHE (UGC-HRDC)University Of Delhi Attending Orientation Programme
Honors and Awards
Name of the Award Awarding Body Award Category Level Award Date
DST Inspire Science Camp DST INSPIRE Extension National 25-09-2014
UGC NEW DELHI CPDHE, University of Delhi Extension National 14-01-2013
UGC NEW DELHI CPDHE, University of Delhi Extension National 15-09-2022
Department of Physical Sciences SGT University, Gurugram, Haryana Extension National 19-03-2016
UGC New Delhi CPDHE -HRDC University of Delhi Extension National 16-01-2013
Talk Poster Presented
Name of the Activity Role Date of Activity
Structure of shock wave by continuum versus kinetic mode Invited Talk 25-11-2018
Solitary wave and travelling wave solution Invited Talk 21-10-2016
Variational iteration method: Theory and Application Invited Talk 16-10-2016
Shock wave structure in a viscous non ideal gas under heat conduction and radiation heat flux Oral Presentation 14-02-2017
Exact solution of shock wave structure in a non ideal gas under constant and variable coefficient of viscosity and heat- conductivity Oral Presentation 27-04-2017
Non-linear wave equation and solitons Invited Talk 24-07-2016
Solitary patterns solution of gZK-BBM nonlinear evolution equation via variational iteration method Oral Presentation 23-07-2016
An application of homotopy perturbation method for modified boundary boundary layer equations over a flat plate Oral Presentation 12-04-2016
Homotopy Perturbation Method: Theory and Application Invited Talk 13-04-2016
Solution of system of gas dynamic equation for the unsteady adiabatic flow by Adomian decomposition method Oral Presentation 26-02-2016
Homotopy analysis method for the solution of the system of unsteady gas flow Oral Presentation 18-12-2015
Similarity Solution for a cylindrical Shock Wave in a Self-gravitating, Rotating and axisymmetric dusty gas with heat conduction and radiation Oral Presentation 21-02-2014
Adomian Decomposition Method: a new approach to Partial Differential Equations Invited Talk 22-02-2014
The Dimensional Analysis and its Application Invited Talk 24-02-2013
A Self-similar flow of a mixture of nonideal gas and small solid particles behind an exponential shock Oral Presentation 12-03-2012
Self-similar adiabatic flow headed by a cylindrical shock wave in a rotating dusty gas Oral Presentation 23-02-2008
Self-similar flow behind a shock wave in a dusty gas with gravitational field Oral Presentation 17-03-2007
Delivered an invited talk on " Lattice Boltzmann method and its Applications in fluid Dynamics" Speaker 03-12-2023
Invited Talk on Existence and Uniqueness of Solution of IVP, at UGC-Human Resource Development Centre, Guru Ghasidas Vishwavidyalaya, Bilaspur, India Speaker 15-01-2024
An invited talk on 'Stability Analysis of Solution of IVPs', UGC-Human Resource Development Centre, Guru Ghasidas Vishwavidyalaya, Bilaspur, India Speaker 16-01-2024
An invited talk at the Department of Mathematics, Rajdhani College, University of Delhi, Delhi, India Speaker 02-05-2024
Well-posed Problem in Differential Equations, Department of Mathematics, Daulat Ram College, University of Delhi, Delhi, India, March 5, 2025 Speaker 05-03-2025
An invited talk on 'Conservation Laws, Characteristics and Shocks', Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi, India, March 26, 2025 Speaker 26-03-2025
It was the launch of the book Ramanujan: Journey of a Great Mathematician, followed by a panel discussion on the legacy of Ramanujan. I participated as a Mathematician in the panel at the event. Panelist 30-04-2025
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