N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions-Reference-Cited by-同舟云学术

N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions

Published:2021-03-01 Issue:0 Volume:0 Page:
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Ma Wen-Xiu¹²³⁴⁵

Affiliation:

1. Department of Mathematics , Zhejiang Normal University , Jinhua 321004 , Zhejiang , China

2. Department of Mathematics , King Abdulaziz University , Jeddah 21589 , Saudi Arabia

3. Department of Mathematics and Statistics , University of South Florida , Tampa , FL 33620-5700 , USA

4. School of Mathematics , South China University of Technology , Guangzhou 510640 , China

5. School of Mathematical and Statistical Sciences , North-West University, Mafikeng Campus, Private Bag X2046 , Mmabatho 2735 , South Africa

Abstract

Abstract We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2020-0214/pdf

Reference25 articles.

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3. S. P. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method, New York, Consultants Bureau, 1984.

4. R. Hirota, Direct Method in Soliton Theory, Cambridge, Cambridge University Press, 2004.

5. R. Hirota, “A new form of Bäcklund transformations and its relation to the inverse scattering problem,” Prog. Theor. Phys., vol. 52, pp. 1498–1512, 1974. https://doi.org/10.1143/ptp.52.1498.

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