Applications of the Sub Equation Method for the High Dimensional Nonlinear Evolution Equation

Applying bilinear form and extended three-wavetype of ansätz approach on the (2+1)-dimensional Sawada-Kotera equation, we obtain new multisoliton solutions, including the double periodic-type three-wave solutions, the breather two-soliton solutions, the double breather soliton solutions, and the three-solitary solutions. These results show that the high-dimensional nonlinear evolution equation has rich dynamical behavior.

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A Generalized F -expansion Method and Its Application in High-Dimensional Nonlinear Evolution Equation

Communications in Theoretical Physics ◽

10.1088/6102/44/2/307 ◽

2005 ◽

Vol 44 (2) ◽

pp. 307-310 ◽

Cited By ~ 11

Author(s):

Jiang Chen ◽

Hong-Sheng He ◽

Kong-Qing Yang

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Expansion Method ◽

High Dimensional

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A novel modified simple equation method and its application to some nonlinear evolution equation systems

10.1063/1.4893799 ◽

2014 ◽

Cited By ~ 5

Author(s):

Ahmet Bekir ◽

Melike Kaplan ◽

Özkan Güner

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Simple Equation ◽

Equation Method ◽

Modified Simple Equation Method

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Application of Exp-function method to high-dimensional nonlinear evolution equation

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2006.11.014 ◽

2008 ◽

Vol 38 (1) ◽

pp. 270-276 ◽

Cited By ~ 102

Author(s):

Sheng Zhang

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Function Method ◽

Nonlinear Evolution ◽

High Dimensional

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Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107301 ◽

2021 ◽

pp. 107301

Author(s):

Yuan Shen ◽

Bo Tian

Keyword(s):

Evolution Equation ◽

Shallow Water ◽

Water Waves ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Soliton Solutions ◽

Bäcklund Transformations ◽

Shallow Water Waves ◽

Backlund Transformations

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Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics

Results in Physics ◽

10.1016/j.rinp.2021.104453 ◽

2021 ◽

pp. 104453

Author(s):

Sachin Kumar ◽

Hassan Almusawa ◽

Ihsanullah Hamid ◽

M.A. Abdou

Keyword(s):

Evolution Equation ◽

Plasma Physics ◽

Closed Form ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Closed Form Solutions ◽

Fifth Order

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Existence results for a nonlinear evolution equation containing a composition of two monotone operators

GAMM-Mitteilungen ◽

10.1002/gamm.201110011 ◽

2011 ◽

Vol 34 (1) ◽

pp. 70-75

Author(s):

Nataliya Kraynyukova

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Monotone Operators ◽

Existence Results

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The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2012.02.019 ◽

2012 ◽

Vol 45 (6) ◽

pp. 846-852 ◽

Cited By ~ 15

Author(s):

V.O. Vakhnenko ◽

E.J. Parkes

Keyword(s):

Evolution Equation ◽

Spectral Data ◽

Inverse Scattering ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Inverse Scattering Method ◽

Singular Solutions ◽

Scattering Method ◽

Continuous Part

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New application of -expansion method to a nonlinear evolution equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.03.048 ◽

2010 ◽

Vol 216 (7) ◽

pp. 2137-2144 ◽

Cited By ~ 7

Author(s):

Yulan Ma ◽

Bangqing Li

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Expansion Method

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Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

10.21203/rs.3.rs-996320/v1 ◽

2021 ◽

Author(s):

Hongcai Ma ◽

Shupan Yue ◽

Yidan Gao ◽

Aiping Deng

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Three Dimensional ◽

Soliton Solutions ◽

Bilinear Method ◽

Test Function ◽

Lump Solutions ◽

Hirota Bilinear ◽

Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

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