Nonlocal symmetry analysis, exact solutions, and evolution of nonlinear waves for one-dimensional shallow water magnetohydrodynamics equations Anupriya Topno, Subhankar Sil, T. Raja Sekhar Physics of Fluids, 2025 In this article, we study the symmetry analysis for a system of hyperbolic quasilinear partial differential equations (PDEs) that describe one-dimensional shallow water magnetohydrodynamics (SMHD) and examine its evolutionary behavior of nonlinear waves. The governing system of PDEs admits a five-dimensional solvable Lie algebra. We construct the optimal system of one-dimensional subalgebras with the help of its adjoint actions. We obtain various closed-form exact solutions by using each of these subalgebras. Furthermore, we establish several nonlocal symmetries of the given system by both the conservation law-based method and the symmetry-based method. Nonlocal symmetries are helpful in finding new exact solutions beyond those of local symmetry reductions. As an application, we study one of the obtained exact solutions of the governing system to analyze the evolutionary behavior of weak discontinuity and its interaction with characteristic shock.
New Results on a Class of Reaction–Convection–Diffusion Equations Through Potential Symmetry Analysis Subhankar Sil, Ch. Srinivasa Rao Mathematical Methods in the Applied Sciences, 2025 In this article, we study the classification of nonlocal symmetries for a class of reaction–convection–diffusion equations. We classify the equations for various choices of the arbitrary functions involved, representing different conservation laws of the equations. We construct equivalent systems called nonlocally related potential systems using these conservation laws. We determine several new nonlocal symmetries for the model equations using these potential systems. These nonlocal symmetries yield some new exact solutions for the equations.
Exact solutions and wave interactions for one-dimensional two-phase thin film model of a perfectly soluble antisurfactant HO Jangid, S Sil, TR Sekhar International Journal of Non-Linear Mechanics, 105262 , 2025 2025 Citations: 2
Non-invertible mappings of linear PDEs to nonlinear PDEs through the symmetry-based method S Sil, G Bluman Journal of Mathematical Analysis and Applications, 130038 , 2025 2025 Citations: 2
Nonlocal symmetry analysis, exact solutions, and evolution of nonlinear waves for one-dimensional shallow water magnetohydrodynamics equations A Topno, S Sil, T Raja Sekhar Physics of Fluids 37 (8) , 2025 2025 Citations: 3
New Results on a Class of Reaction–Convection–Diffusion Equations Through Potential Symmetry Analysis S Sil, C Srinivasa Rao Mathematical Methods in the Applied Sciences 48 (9), 10096-10109 , 2025 2025 Citations: 2
On the Lie symmetry analysis of three-dimensional perturbed shear flows S Mandal, S Sil, S Ghosh Chaos, Solitons & Fractals 191, 115875 , 2025 2025 Citations: 7
Lie symmetries and optimal classifications with certain modal approaches for the three-dimensional gas-dynamical equations S Mandal, S Sil, S Ghosh Chaos, Solitons & Fractals 181, 114672 , 2024 2024 Citations: 6
Nonclassical symmetries, nonlinear self-adjointness, conservation laws and some new exact solutions of cylindrical KdV equation S Sil International Journal of Applied and Computational Mathematics 9 (5), 69 , 2023 2023 Citations: 4
Application of symmetry analysis to viscoelastic fluid model S Shagolshem, B Bira, S Sil Communications in Nonlinear Science and Numerical Simulation 125, 107417 , 2023 2023 Citations: 12
Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution S Sil, TR Sekhar Applied Mathematics and Computation 440, 127660 , 2023 2023 Citations: 23
Conservation laws and some new exact solutions for traffic flow model via symmetry analysis S Shagolshem, B Bira, S Sil Chaos, Solitons & Fractals 165, 112779 , 2022 2022 Citations: 12
Nonlocal conservation laws and dynamics of soliton solutions of (2+ 1)-dimensional Boiti–Leon–Pempinelli system S Sil, T Raja Sekhar Physics of Fluids 34 (11) , 2022 2022 Citations: 16
Symmetry reductions and exact solutions of two new generalized negative KdV type equations S Sil, P Guha Journal of Geometry and Physics 178, 104558 , 2022 2022 Citations: 5
Symmetries, Conservation Laws and Exact Solutions of Certain Nonlinear Partial Differential Equations S Sil IIT Kharagpur , 2022 2022
Nonclassical symmetry analysis, conservation laws of one-dimensional macroscopic production model and evolution of nonlinear waves S Sil, TR Sekhar Journal of Mathematical Analysis and Applications 497 (1), 124847 , 2021 2021 Citations: 41
Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation S Sil, TR Sekhar, D Zeidan Chaos, Solitons & Fractals 139, 110010 , 2020 2020 Citations: 54
Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model S Sil, T Raja Sekhar The European Physical Journal Plus 135 (6), 514 , 2020 2020 Citations: 29
MOST CITED SCHOLAR PUBLICATIONS
Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation S Sil, TR Sekhar, D Zeidan Chaos, Solitons & Fractals 139, 110010 , 2020 2020 Citations: 54
Nonclassical symmetry analysis, conservation laws of one-dimensional macroscopic production model and evolution of nonlinear waves S Sil, TR Sekhar Journal of Mathematical Analysis and Applications 497 (1), 124847 , 2021 2021 Citations: 41
Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model S Sil, T Raja Sekhar The European Physical Journal Plus 135 (6), 514 , 2020 2020 Citations: 29
Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution S Sil, TR Sekhar Applied Mathematics and Computation 440, 127660 , 2023 2023 Citations: 23
Nonlocal conservation laws and dynamics of soliton solutions of (2+ 1)-dimensional Boiti–Leon–Pempinelli system S Sil, T Raja Sekhar Physics of Fluids 34 (11) , 2022 2022 Citations: 16
Application of symmetry analysis to viscoelastic fluid model S Shagolshem, B Bira, S Sil Communications in Nonlinear Science and Numerical Simulation 125, 107417 , 2023 2023 Citations: 12
Conservation laws and some new exact solutions for traffic flow model via symmetry analysis S Shagolshem, B Bira, S Sil Chaos, Solitons & Fractals 165, 112779 , 2022 2022 Citations: 12
On the Lie symmetry analysis of three-dimensional perturbed shear flows S Mandal, S Sil, S Ghosh Chaos, Solitons & Fractals 191, 115875 , 2025 2025 Citations: 7
Lie symmetries and optimal classifications with certain modal approaches for the three-dimensional gas-dynamical equations S Mandal, S Sil, S Ghosh Chaos, Solitons & Fractals 181, 114672 , 2024 2024 Citations: 6
Symmetry reductions and exact solutions of two new generalized negative KdV type equations S Sil, P Guha Journal of Geometry and Physics 178, 104558 , 2022 2022 Citations: 5
Nonclassical symmetries, nonlinear self-adjointness, conservation laws and some new exact solutions of cylindrical KdV equation S Sil International Journal of Applied and Computational Mathematics 9 (5), 69 , 2023 2023 Citations: 4
Nonlocal symmetry analysis, exact solutions, and evolution of nonlinear waves for one-dimensional shallow water magnetohydrodynamics equations A Topno, S Sil, T Raja Sekhar Physics of Fluids 37 (8) , 2025 2025 Citations: 3
Exact solutions and wave interactions for one-dimensional two-phase thin film model of a perfectly soluble antisurfactant HO Jangid, S Sil, TR Sekhar International Journal of Non-Linear Mechanics, 105262 , 2025 2025 Citations: 2
Non-invertible mappings of linear PDEs to nonlinear PDEs through the symmetry-based method S Sil, G Bluman Journal of Mathematical Analysis and Applications, 130038 , 2025 2025 Citations: 2
New Results on a Class of Reaction–Convection–Diffusion Equations Through Potential Symmetry Analysis S Sil, C Srinivasa Rao Mathematical Methods in the Applied Sciences 48 (9), 10096-10109 , 2025 2025 Citations: 2
Symmetries, Conservation Laws and Exact Solutions of Certain Nonlinear Partial Differential Equations S Sil IIT Kharagpur , 2022 2022
