Two-dimensional symmetry reduction of (2+1)-dimensional nonlinear Klein–Gordon equation

Hu, Xiaoguang; Chen, Yong

doi:10.1016/j.amc.2009.06.049

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…In literature, there are many techniques available for obtaining optimal systems and a lot of excellent work has been done by experts e.g. [3,[5][6][7][8][9][10][11]13,18,[20][21][22][23]. Here, we use Peter J. Olver's technique [19] to derive optimal system for different cases of Monge-Ampere equation by assuming different particular values of the non-homogeneous part f (x, y).…”

Section: Introductionmentioning

confidence: 99%

Optimal System and Exact Solutions of Monge-Ampere Equation

Ферозе

Umair²

2021

Comm. Math. Appl.

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A solution that remains unchanged when transformed under Lie group of point symmetries of the differential equation is an invariant solution of the differential equation. Optimal system of Lie group of point symmetry generators provide all possible invariant solutions of differential equation. Here, using optimal system of Lie point symmetry generators group invariant solutions are obtained. Using these solutions, exact solutions of non-homogeneous Monge-Ampere equation have been presented here.

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Section: Introductionmentioning

confidence: 99%

Optimal System and Exact Solutions of Monge-Ampere Equation

Ферозе

Umair²

2021

Comm. Math. Appl.

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“…Since it only depends on fragments of the theory of Lie algebras, Olver's method as developed here has the feature of being very elementary. Based on Olver's method, we have also constructed many interesting and important invariant solutions [9][10][11][12][13] for a number of systems of PDEs in atmosphere and geometric field. However, as Olver said, although some sophisticated techniques are available for Lie algebras with additional structure, in essence this problem is attacked by the naïve approach.…”

Section: Introductionmentioning

confidence: 99%

A direct algorithm of one-dimensional optimal system for the group invariant solutions

Chen

2015

Journal of Mathematical Physics

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116

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A direct and systematic algorithm is proposed to find one-dimensional optimal system for the group invariant solutions, which is attributed to the classification of its corresponding one-dimensional Lie algebra. Since the method is based on different values of all the invariants, the process itself can both guarantee the comprehensiveness and demonstrate the inequivalence of the optimal system, with no further proof. To illustrate our method more clearly , we give a couple of well-known examples: the Korteweg-de Vries (KdV) equation and the heat equation.

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