2020
DOI: 10.1142/s0219887821500286
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Solitary wave solutions of mKdV–Calogero–Bogoyavlenskii–Schiff equation by using Lie symmetry analysis

Abstract: In this paper, we introduced and established some group invariant results of [Formula: see text]-dimensional mKdV–Calogero–Bogoyavlenskii–Schiff equation. Using the one-parameter Lie-group of transformations, we explored various closed-form solutions. The procedure minimizes the number of independent variables by one in every proceeding stage leading to form a system of the ordinary differential equations. The nature of solutions is investigated both analytically and physically through their evolutionary profi… Show more

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Cited by 14 publications
(4 citation statements)
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“…These invariant solutions describe their behavior like they display its asymptotic nature and the information of the singularities if it exists. Thus, various efficient methods and techniques are there to obtain exact soliton solutions, such as inverse scattering transformation [1], Hirota bilinear method [2], nonlocal symmetry [3], Bäcklund transformation [3], Painlevé analysis [3], Lie symmetry method [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], etc.…”
Section: Introductionmentioning
confidence: 99%
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“…These invariant solutions describe their behavior like they display its asymptotic nature and the information of the singularities if it exists. Thus, various efficient methods and techniques are there to obtain exact soliton solutions, such as inverse scattering transformation [1], Hirota bilinear method [2], nonlocal symmetry [3], Bäcklund transformation [3], Painlevé analysis [3], Lie symmetry method [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], etc.…”
Section: Introductionmentioning
confidence: 99%
“…Using similarity transformation method(STM) [21], some invariant solutions are constructed. However, the optimal subalgebras constructed for equation (1.1) and the derivation for the invariant solutions of mBSchiff equation can also be found in [7-9, 12, 13].…”
Section: Introductionmentioning
confidence: 99%
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“…Several researchers and mathematicians have paid much attention to obtaining exact rational solutions and closed-form solutions of numerous nonlinear models of NLEE. In the process of doing so, various powerful and efficient analytical mathematical methods have been developed for finding exact analytical solutions, for example, the Bäcklund transformation method [1], the Darboux transformations method [2], the inverse-scattering method [3], the Hirota bilinear method [4], the auxiliary equation method [5], the exp-function method [6], the Lie symmetry method [7][8][9][10][11], the modified F-expansion method [12], modified simple equation methods [13], the ¢ G G ( ) -expansion method [14,15], the generalized exponential rational function method [16,17], and so on. Closed-form solutions of NLEEs play a significant role in our understanding of the dynamical structures and characteristic properties of various nonlinear models.…”
Section: Introductionmentioning
confidence: 99%