Access the full text.
Sign up today, get DeepDyve free for 14 days.
Y. Hua, B. Guo, W. Ma, W. Ma, W. Ma, Xing Lü (2019)
Interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation for nonlinear wavesApplied Mathematical Modelling
A. Wazwaz (2014)
New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutionsCentral European Journal of Engineering, 4
J. Patera, P. Winternitz, H. Zassenhaus (1975)
Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré groupJournal of Mathematical Physics, 16
P. Olver (1986)
Applications of lie groups to differential equationsActa Applicandae Mathematica, 20
Kajal Sharma, R. Arora, A. Chauhan (2020)
Invariance analysis, exact solutions and conservation laws of (2+1)-dimensional dispersive long wave equationsPhysica Scripta, 95
Zhaqilao (2013)
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equationPhysics Letters A, 377
A. Chauhan, Kajal Sharma, R. Arora (2020)
Lie symmetry analysis, optimal system, and generalized group invariant solutions of the (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa equationMathematical Methods in the Applied Sciences, 43
L. Vogler (2016)
The Direct Method In Soliton Theory
Mei-Dan Chen, Xian Li, Yao Wang, Biao Li (2017)
A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution EquationCommunications in Theoretical Physics, 67
R. Hirota, Masaaki Ito (1983)
Resonance of Solitons in One DimensionJournal of the Physical Society of Japan, 52
O. Makinde, I. Animasaun (2016)
Thermophoresis and Brownian motion effects on MHD bioconvection of nanofluid with nonlinear thermal radiation and quartic chemical reaction past an upper horizontal surface of a paraboloid of revolutionJournal of Molecular Liquids, 221
(2014)
Group analysis of di erential equations
Yaning Tang, Siqiao Tao, Meiling Zhou, Qing Guan (2017)
Interaction solutions between lump and other solitons of two classes of nonlinear evolution equationsNonlinear Dynamics, 89
A. Wazwaz (2013)
A variety of distinct kinds of multiple soliton solutions for a ( 3 + 1)‐dimensional nonlinear evolution equationMathematical Methods in the Applied Sciences, 36
Z. Ayati, K. Hosseini, M. Mirzazadeh (2017)
Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solidsNonlinear Engineering, 6
R. Hirota, J. Satsuma (1976)
N-Soliton Solutions of Model Equations for Shallow Water WavesJournal of the Physical Society of Japan, 40
Sachin Kumar, Dharmendra Kumar, A. Wazwaz (2019)
Group invariant solutions of (3+1)-dimensional generalized B-type Kadomstsev Petviashvili equation using optimal system of Lie subalgebraPhysica Scripta, 94
O. Makinde, I. Animasaun (2016)
Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolutionInternational Journal of Thermal Sciences, 109
R. Hirota (1971)
Exact solution of the Korteweg-deVries equation for multiple collision of solitons
M. El-Borai, H. El-Owaidy, H. Ahmed, A. Arnous, M. Mirzazadeh (2017)
Solitons and other solutions to the coupled nonlinear Schrödinger type equationsNonlinear Engineering, 6
Xiaorui Hu, Yuqi Li, Yong Chen (2014)
A direct algorithm of one-dimensional optimal system for the group invariant solutionsarXiv: Group Theory
Wu Jian-Ping (2011)
A New Wronskian Condition for a (3+1)-Dimensional Nonlinear Evolution EquationChinese Physics Letters, 28
N. Khan, Fatima Riaz, Asmat Ara (2016)
A note on soliton solutions of Klein-Gordon-Zakharov equation by variational approachNonlinear Engineering, 5
R. Hirota (1974)
A New Form of Bäcklund Transformations and Its Relation to the Inverse Scattering ProblemProgress of Theoretical Physics, 52
Xin Zhao, B. Tian, He-Yuan Tian, Dan-Yu Yang (2021)
Bilinear Bäcklund transformation, Lax pair and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physicsNonlinear Dynamics, 103
X. Geng (2003)
Algebraic-geometrical solutions of some multidimensional nonlinear evolution equationsJournal of Physics A: Mathematical and General, 36
Hu Xiao (2011)
Symmetry Groups and Exact Solutions of a (3+1)-dimensional Nonlinear Evolution Equation and Maccari's SystemJournal of Ningbo University
X. Geng, Yunling Ma (2007)
N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equationPhysics Letters A, 369
J. Patera, R. Sharp, P. Winternitz, H. Zassenhaus (1976)
Invariants of real low dimension Lie algebrasJournal of Mathematical Physics, 17
A. Wazwaz (2009)
A (3 + 1)-dimensional nonlinear evolution equation with multiple soliton solutions and multiple singular soliton solutionsAppl. Math. Comput., 215
K. Chou, Guan-Xin Li, C. Qu (2001)
A Note on Optimal Systems for the Heat EquationJournal of Mathematical Analysis and Applications, 261
Yu-bin Shi, Yi Zhang (2017)
Rogue waves of a (3+1)-dimensional nonlinear evolution equationCommun. Nonlinear Sci. Numer. Simul., 44
A. Wazwaz (2015)
New (3+1)-dimensional nonlinear evolution equations with mKdV equation constituting its main part: Multiple soliton solutionsChaos Solitons & Fractals, 76
J. Hietarinta (1987)
A Search for Bilinear Equations Passing Hirota''s Three-Soliton Condition
Masaaki Ito (1980)
An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher OrdersJournal of the Physical Society of Japan, 49
AbstractStudies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used to apply the similarity reduction and to find some exact solutions of a (3+1) dimensional nonlinear evolution equation. In this report, the groups of symmetries, Tables for commutation, and adjoints with infinitesimal generators were established. The subalgebra and its optimal system is obtained with the aid of the adjoint Table. Moreover, the equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves.
Nonlinear Engineering – de Gruyter
Published: Jan 1, 2021
Keywords: (3 + 1) - dimensional nonlinear evolution equation; optimal system; Lie symmetry analysis; group invariant solutions
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.