Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier–Stokes equation

Jiwari, Ram; Kumar, Vikas; Singh, Salvinder Singh Karam

doi:10.1007/s00366-020-01175-9

Cited by 27 publications

(8 citation statements)

References 36 publications

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“…Schrödinger Equation e purpose of this Section 2 is to establish the invariance condition for hyperbolic Schrödinger equation in [23]. is invariant condition plays a crucial role in the Lie symmetry analysis method.…”

Section: Lie Symmetry Analysis For Hyperbolicmentioning

confidence: 99%

“…erefore, (2 + 1)-dimensional hyperbolic equation ( 17) can be reduced into the (1 + 1)-dimensional hyperbolic partial differential equation with suitable transformation (23) as follows:…”

Section: Reduced (1 + 1)-dimensional Equation For Equation (17) Under...mentioning

confidence: 99%

“…, where μ is an arbitrary constant. Further, substituting equation ( 28) into the similarity solutions (23) and using the form of similarity variables z 1 and z 2 , the solution of the hyperbolic Schrödinger equation ( 17) is given as follows:…”

Section: Reduced Ordinary Differential Equation and Complex Solution ...mentioning

confidence: 99%

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Hyperbolic (3+1)‐Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability

Kumar¹,

Jiwari

Djurayevich

et al. 2022

Journal of Mathematics

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The hyperbolic nonlinear Schrödinger equation in the (3 + 1)-dimension depicts the evolution of the elevation of the water wave surface for slowly modulated wave trains in deep water. Many researchers have studied the applicability and practicality of this model, but the analytical approach has been virtually absent from the literature. We adapted the lie symmetry analysis method to obtain a new complex solution in this work. The obtained complex solution contains bright and dark solitons. Furthermore, modulation instability is applied to this model to explain the interplay between nonlinear and dispersive effects. As a result, the modulation instability condition and the explosive rate are also discussed.

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Section: Lie Symmetry Analysis For Hyperbolicmentioning

confidence: 99%

“…erefore, (2 + 1)-dimensional hyperbolic equation ( 17) can be reduced into the (1 + 1)-dimensional hyperbolic partial differential equation with suitable transformation (23) as follows:…”

Section: Reduced (1 + 1)-dimensional Equation For Equation (17) Under...mentioning

confidence: 99%

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Hyperbolic (3+1)‐Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability

Kumar¹,

Jiwari

Djurayevich

et al. 2022

Journal of Mathematics

Self Cite

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“…The authors in the literature [35, 36] used the Lie symmetry analysis to find some new exact solutions of the

\left(3&#x0002B;1\right)

‐dimensional non‐linear water wave equation in liquid with gas bubbles and

\left(2&#x0002B;1\right)

‐dimensional modified dispersive water wave (MDWW) equation. The authors found novel and precise solutions of compressible isentropic Navier–Stokes equation utilizing optimal subalgebras in Jiwari et al [37]. Sil and Raja Sekhar [38] find accurate solutions for an integrable soliton problem via non‐local symmetry.…”

Section: Introductionmentioning

confidence: 99%

Invariance analysis, optimal system, and group invariant solutions of (3+1)‐dimensional non‐linear MA‐FAN equation

Sharma

Yadav

Arora

2023

Math Methods in App Sciences

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The importance of research on non‐linear evolution equations has increased over time. In the fields of plasma physics, fluid mechanics, optical fibers, and other sciences, such equations are not unrealistic. Discovering the exact answers to these equations needs to be a top priority. In this study, we will investigate a ‐dimensional non‐linear MA‐FAN equation that is used to simulate weakly non‐linear restoring forces and frequency dispersion in long wavelength water waves. The ‐dimensional MA‐FAN equation's solution is analyzed using the Lie symmetry analysis, and it is also used to pick the appropriate one‐dimensional Lie subalgebra system. We discover invariant solutions of the ‐dimensional MA‐FAN equation, which may capture the dynamic behavior of non‐linear waves, by solving the numerous ordinary differential equations that are reduced equations from the MA‐FAN equation by using the Lie group of transformation approach. In conclusion, the method offered is robust and convenient tool for studying various classes of non‐linear PDE solutions.

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“…ere are several technical methods for solving and investigating several kind of nonlinear partial differential equations, e.g. [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Elmandouh

Elbrolosy

2022

Journal of Mathematics

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The Ivancevic option pricing model comes as an alternative to the Black-Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. The applicability and practicality of this model have been studied by many researchers, but the analytical approach has been virtually absent from the literature. This study intends to examine some dynamic features of this model. By using the well-known ARS algorithm, it is demonstrated that this model is not integrable in the Painlevé sense. He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright-like soliton, kinky-bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. Furthermore, we introduce a classification of the wave solutions into periodic, super periodic, kink, and solitary solutions according to the type of the phase plane orbits. Some 3D-graphical representations of some of the obtained solutions are displayed. The influence of the model’s parameters on the obtained wave solutions is discussed and clarified graphically.

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Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier–Stokes equation

Cited by 27 publications

References 36 publications

Hyperbolic (3+1)‐Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability

Hyperbolic (3+1)‐Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability

Invariance analysis, optimal system, and group invariant solutions of (3+1)‐dimensional non‐linear MA‐FAN equation

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

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