Variational principle, conservation laws and exact solutions for dust ion acoustic shock waves modeling modified Burger equation

El-Kalaawy, Omar H.

doi:10.1016/j.camwa.2016.06.013

Cited by 27 publications

(24 citation statements)

References 34 publications

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“…The variational principle is also the theoretical basis for the variational iteration method, where the general Lagrange multiplier is identified by solving the Euler–Lagrange equations of the correction functional (Anjum and He, 2019; He et al , 2014; Inc et al , 2018; Jafari et al , 2018; Baleanu et al , 2018; Dogan Durgun and Konuralp, 2018). Recently the variational principle was successfully applied to solitary theory (Biswas et al , 2017; El-Kalaawy, 2016; El-Kalaawy, 2017), and it might be also a potential tool for shock identification in a transonic flow.…”

Section: Introductionmentioning

confidence: 99%

Lagrange crisis and generalized variational principle for 3D unsteady flow

2019

HFF

154

104

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Purpose A three-dimensional (3D) unsteady potential flow might admit a variational principle. The purpose of this paper is to adopt a semi-inverse method to search for the variational formulation from the governing equations. Design/methodology/approach A suitable trial functional with a possible unknown function is constructed, and the identification of the unknown function is given in detail. The Lagrange multiplier method is used to establish a generalized variational principle, but in vain. Findings Some new variational principles are obtained, and the semi-inverse method can easily overcome the Lagrange crisis. Practical implications The semi-inverse method sheds a promising light on variational theory, and it can replace the Lagrange multiplier method for the establishment of a generalized variational principle. It can be used for the establishment of a variational principle for fractal and fractional calculus. Originality/value This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.

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Section: Introductionmentioning

confidence: 99%

Lagrange crisis and generalized variational principle for 3D unsteady flow

2019

HFF

154

104

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“…In this section, we consider the exact solutions [25][26][27][28][29] by using the method of conservation laws. For the conservation law of V 2 , from (Section 3.2), we obtain the conservation law of…”

Section: Exact Solutionsmentioning

confidence: 99%

Lie Symmetries, Conservation Laws and Exact Solutions for Jaulent-Miodek Equations

Pei

Bai

2019

Symmetry

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“…Conservation laws are also used in the development of numerical methods to establish the existence and uniqueness of solution. There are many methods of constructing conservation laws for differential equations (DEs) [39][40][41][42][43][44][45]. The well-known Noether theorem [46] establishes a connection between Lie point symmetries and conservation laws of DEs, provided that the equations are Euler-Lagrange equations.…”

Section: Introductionmentioning

confidence: 99%

Conservation laws, analytical solutions and stability analysis for the time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation

et al. 2019

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In this paper, we consider the (3 + 1)-dimensional time-fractional Schamel-Zakharov-Kuznetsov-Burgers (SZKB) equation. With the help of the Riemann-Liouville derivatives, the Lie point symmetries of the (3 + 1)-dimensional time-fractional SZKB equation are derived. By applying the Lie point symmetry method as well as Erdélyi-Kober fractional operator, we get the similarity reductions of the time-fractional SZKB equation. Conservation laws of the time-fractional SZKB are constructed. Moreover, we obtain its power series solutions with the convergence analysis. In addition, the analytical solution is obtained by modified trial equation method. Finally, stability is analyzed graphically in different planes.

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Variational principle, conservation laws and exact solutions for dust ion acoustic shock waves modeling modified Burger equation

Cited by 27 publications

References 34 publications

Lagrange crisis and generalized variational principle for 3D unsteady flow

Lagrange crisis and generalized variational principle for 3D unsteady flow

Lie Symmetries, Conservation Laws and Exact Solutions for Jaulent-Miodek Equations

Conservation laws, analytical solutions and stability analysis for the time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation

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