Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model

Sil, Subhankar; Sekhar, T. RajaÂ

doi:10.1140/epjp/s13360-020-00530-5

Cited by 21 publications

(6 citation statements)

References 33 publications

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“…More specifically, the singular δ-standing wave was found by Sun [39] when the Riemann problem for (1.1) was considered under the situation p(ρ) = ρ. Furthermore, some new exact solutions for (1.1) in the case of p(ρ) = ρ have also been obtained by Sil and Raja Sekhar [37,38] with the help of nonclassical symmetry analysis as well as interactions of nonlinear waves have been widely investigated by Minhajul and Raja Sekhar [21]. Very recently, exact Riemann solutions have been obtained and wave interactions have been dealt with carefully in [43] for (1.1) by taking the pressure-density relation p(ρ) = − 1 ρ for Chaplygin gas.…”

Section: Introductionmentioning

confidence: 80%

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

Shan

Shen²,

Wei³

2022

Math. Model. Nat. Phenom.

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The exact Riemann solutions for the extended macroscopic production model with an adiabatic exponent are constructed in perfectly explicit forms. The asymptotic limit of Riemann solution consisting of 1-shock wave and 2-contact discontinuity tends to a delta shock solution for the pressureless gas dynamics model under the special over-compressive entropy condition as the adiabatic exponent drops to one. In contrast, the asymptotic limit of Riemann solution composed of 1-rarefaction wave and 2-contact discontinuity tends to the vacuum solution surrounded by two contact discontinuities by letting the adiabatic exponent tend to one, in which the state in the interior of the 1-rarefaction wave fan is developed into vacuum. The intrinsic phenomena of concentration and cavitation are identified and investigated carefully during this limiting process, which displays more complicated and completely different behavior compared with previous literature. In addition, some representative numerical calculations are also provided, which are in well agreement with our theoretical results.

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Section: Introductionmentioning

confidence: 80%

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

Shan

Shen²,

Wei³

2022

Math. Model. Nat. Phenom.

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“…It is observed that the system admits infinite dimensional Lie algebra. We performed the classification of optimal subalgebras and using each subalgebra we obtained several new exact solutions ((5), ( 6), ( 8), ( 9), ( 11), ( 12), ( 13), ( 14), ( 16), (18), (19), (20), (21), (24), (25) and ( 26)) of the BLP system. In addition to that, we noticed that the only solution (22) presented in [33] was recovered as a particular case of the obtained solution (20).…”

Section: Discussionmentioning

confidence: 99%

“…A PDE may have more than one conservation law which arises by multiplying appropriate multipliers [17,18,19] to the given PDE. Recently, Sil et al [20,21] applied direct multipliers method to construct conservation laws and applied them to study nonlocal symmetry analysis.…”

Section: Introductionmentioning

confidence: 99%

Similarity reductions, new traveling wave solutions, conservation laws of (2+1)- dimensional Boiti-Leon-Pempinelli system

Sil,

Sekhar

2021

Preprint

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In this article we obtain exact solutions of (2+1)-dimensional Boiti-Leon-Pempinelli system of nonlinear partial differential equations which describes the evolution of horizontal velocity component of water waves propagating in two directions. We perform the Lie symmetry analysis to the given system and construct one-dimensional optimal subalgebra which involves some arbitrary functions of spatial variables. Several new exact solutions are obtained by symmetry reduction using each of the optimal subalgebra. We then study the physical behavior of some exact solutions by numerical simulations and observed many interesting phenomena such as traveling waves, lump type solitons, kink and anti-kink type solitons, breather solitons, singular kink type solitons and etc. We construct several conservation laws of the system by using multipliers method. As an application, we study the nonlocal conservation laws of the system by constructing potential systems and appending gauge constraints.

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“…Very recently, the interactions of nonlinear waves for this macroscopic production model have also been investigated carefully by Manhajul and Raja Sekhar 35 with the help of the hodograph transformation in connection with the technique of differential constraints. Also see Sil and Raja Sekhar 36,37 about the symmetry analysis of this model (). Hence, it is natural and also necessary to investigate the limits of Riemann solutions for the perturbed macroscopic production model for the actual comparisons of dynamical behaviors among different macroscopic production models.…”

Section: Introductionmentioning

confidence: 99%

The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model

Zhang

Sun

2021

Math Methods in App Sciences

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The exact solutions of the Riemann problems for the two different perturbed macroscopic production models are considered and constructed, respectively, for all the possible cases. It is found that the asymptotic limits of solutions to the Riemann problem for the first kind of perturbed macroscopic production model do not converge to those of the pressureless gas dynamics model, because the delta shock wave in the limiting situation has different propagation speed and strength from those for the pressureless gas dynamics model. In order to remedy it, the second kind of perturbed macroscopic production model is proposed, whose asymptotic limits of Riemann solutions are identical with those of the pressureless gas dynamics model.

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Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model

Cited by 21 publications

References 33 publications

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

Similarity reductions, new traveling wave solutions, conservation laws of (2+1)- dimensional Boiti-Leon-Pempinelli system

The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model

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