Characterizations of all real solutions for the KdV equation and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si3.svg"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:msub></mml:math>

Gu, Yongyi; Wu, Chengfa; Yao, Xiao; Yuan, Wenjun

doi:10.1016/j.aml.2020.106446

Cited by 29 publications

(13 citation statements)

References 18 publications

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“…In recent years, many mathematicians and physicists studied the nonlinear integrable systems that occur in various fields such as biology, fluid dynamics, quantum and plasma physics, thermal engineering and optics. Plenty of methods have been developed for getting exact solutions to nonlinear differential equations such as the modified extended tanh method [1,2], the improved F-expansion method [3], the modified simple equation method [4], the complex method [5][6][7][8], the generalized ( ′/ ) G G -expansion method [9][10][11], the exp(− ( )) ψ z -expansion method [12][13][14][15][16], the ( + / ′) m G 1 -expansion method [17], the sine-Gordon expansion method [18][19][20][21][22][23][24], the extended sine-Gordon expansion method [25][26][27], the extended rational sinh-cosh method [28], the modified Kudryashov method [29] and other methods [30][31][32].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Aminakbari

Yuan

2020

Open Mathematics

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In this article, meromorphic exact solutions for the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (gCBS) equation are obtained by using the complex method. With the applications of our results, traveling wave exact solutions of the breaking soliton equation are achieved. The dynamic behaviors of exact solutions of the (2 + 1)-dimensional gCBS equation are shown by some graphs. In particular, the graphs of elliptic function solutions are comparatively rare in other literature. The idea of this study can be applied to the complex nonlinear systems of some areas of engineering.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Aminakbari

Yuan

2020

Open Mathematics

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“…In present work, our goal is to solve the nonlinear fractional Liouville equation by using the extended complex method based on the work of Yuan et al [38][39][40][41][42][43]. This is a beneficial technique to attain exact analytical solutions.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method

Rehman

Yuan

2020

Advances in Mathematical Physics

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The extended complex method is investigated for exact analytical solutions of nonlinear fractional Liouville equation. Based on the work of Yuan et al., the new rational, periodic, and elliptic function solutions have been obtained. By adjusting the arbitrary values to the constants in the constructed solutions, it can describe the physical phenomena to the traveling wave solutions, since traveling wave has significant value in applied sciences and engineering. Our results indicate that the extended complex technique is direct and easily applicable to solve the nonlinear fractional partial differential equations (NLFPDEs).

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“…These are the only meromorphic functions which satisfy the addition formulae. They are also the only meromorphic solutions of certain non-linear complex differential equations (see [10], [4], [5], [6], [19] and [12]).…”

Section: Introductionmentioning

confidence: 99%

Rationality of meromorphic functions between real algebraic sets in the plane

Ng¹,

Xiao²

2022

Preprint

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We study one variable meromorphic functions mapping a planar real algebraic set A to another real algebraic set in the complex plane. By using the theory of Schwarz reflection functions, we show that for certain A, these meromorphic functions must be rational. In particular, when A is the standard unit circle, we obtain an one dimensional analog of Poincaré(1907), Tanaka(1962 and Alexander(1974)'s rationality results for 2m−1 dimensional sphere in C m when m ≥ 2. 2010 Mathematics Subject Classification. 30C99, 30D99.

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Characterizations of all real solutions for the KdV equation and WR

Cited by 29 publications

References 18 publications

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method

Rationality of meromorphic functions between real algebraic sets in the plane

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