The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations

Physics Letters A ◽

10.1016/j.physleta.2004.01.056 ◽

2004 ◽

Vol 323 (1-2) ◽

pp. 77-88 ◽

Author(s):

Yubin Zhou ◽

Mingliang Wang ◽

Tiande Miao

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Periodic Wave ◽

Solitary Wave Solutions ◽

Partial Differential ◽

Periodic Wave Solutions ◽

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Exact periodic wave solutions for some nonlinear partial differential equations

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2005.08.063 ◽

2006 ◽

Vol 29 (4) ◽

pp. 1037-1044 ◽

Author(s):

S.A. El-Wakil ◽

A. Elgarayhi ◽

A. Elhanbaly

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Periodic Wave ◽

Partial Differential ◽

Periodic Wave Solutions ◽

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On solitary wave solutions of a class of nonlinear partial differential equations based on the function1/coshn(αx+βt)

Applied Mathematics and Computation ◽

10.1016/j.amc.2017.07.064 ◽

2017 ◽

Vol 315 ◽

pp. 372-380 ◽

Author(s):

Nikolay K. Vitanov ◽

Zlatinka I. Dimitrova ◽

Tsvetelina I. Ivanova

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Solitary Wave Solutions ◽

Partial Differential ◽

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Comments on “A new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the Exp-function method”

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.06.029 ◽

2014 ◽

Vol 243 ◽

pp. 419-425 ◽

Author(s):

Zenonas Navickas ◽

Minvydas Ragulskis

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Function Method ◽

Nonlinear Partial Differential Equations ◽

Solitary Wave Solutions ◽

Partial Differential ◽

Automatic Computation ◽

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Solitary wave solutions for nonlinear partial differential equations that contain monomials of odd and even grades with respect to participating derivatives

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.08.101 ◽

2014 ◽

Vol 247 ◽

pp. 213-217 ◽

Author(s):

Nikolay K. Vitanov ◽

Zlatinka I. Dimitrova

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Solitary Wave Solutions ◽

Partial Differential ◽

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Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications

Results in Physics ◽

10.1016/j.rinp.2018.11.014 ◽

2018 ◽

Vol 11 ◽

pp. 1161-1171 ◽

Author(s):

Dianchen Lu ◽

Aly R. Seadawy ◽

Mujahid Iqbal

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Coupled System ◽

Solitary Wave Solutions ◽

Mathematical Methods ◽

Partial Differential ◽

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A new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the Exp-function method

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.08.031 ◽

2012 ◽

Vol 219 (4) ◽

pp. 1890-1896 ◽

Author(s):

Lei Zhao ◽

Dingjiang Huang ◽

Shuigeng Zhou

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Function Method ◽

Nonlinear Partial Differential Equations ◽

Solitary Wave Solutions ◽

Partial Differential ◽

Automatic Computation ◽

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Perturbation theory for approximately integrable partial differential equations, and the change of amplitude of solitary-wave solutions of the BBM equation

Journal of Fluid Mechanics ◽

10.1017/s0022112087002416 ◽

1987 ◽

Vol 182 (-1) ◽

pp. 467 ◽

Author(s):

J. G. B. Byatt-Smith

Keyword(s):

Perturbation Theory ◽

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Solitary Wave Solutions ◽

Partial Differential ◽

Wave Solutions ◽

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Solitary wave solutions for some nonlinear time-fractional partial differential equations

Pramana ◽

10.1007/s12043-018-1636-8 ◽

2018 ◽

Vol 91 (5) ◽

Author(s):

S Z Hassan ◽

Mahmoud A E Abdelrahman

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Solitary Wave Solutions ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

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Fractional transformation method for constructing solitary wave solutions to some nonlinear fractional partial differential equations

Applied Mathematical Sciences ◽

10.12988/ams.2014.47593 ◽

2014 ◽

Vol 8 ◽

pp. 5751-5762 ◽

Author(s):

Safwan Al-Shara'

Keyword(s):

Partial Differential Equations ◽

Solitary Wave ◽

Differential Equations ◽

Transformation Method ◽

Solitary Wave Solutions ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

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Solitary Wave Solutions, Periodic Wave Solutions and Folded Localized Excitations for the Dissipative Zabolotskaya-Khokhlov System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.599-601.1712 ◽

2014 ◽

Vol 599-601 ◽

pp. 1712-1715

Author(s):

Qing Bao Ren ◽

Song Hua Ma ◽

Jian Ping Fang

Keyword(s):

Solitary Wave ◽

Exact Solutions ◽

Solitary Wave Solution ◽

Nonlinear Partial Differential Equations ◽

Periodic Wave ◽

Solitary Wave Solutions ◽

Periodic Wave Solutions ◽

Wave Solutions ◽

Mapping Approach ◽

Localized Excitations

The mapping approach is a powerful tool to looking for the exact solutions for nonlinear partial differential equations. In this paper, using an improved mapping approach, a series of exact solutions (including solitary wave solutions and periodic wave solutions) of the (2+1)-dimensional dissipative Zabolotskaya Khokhlov (DZK) system is derived. Based on the derived solitary wave solution, we obtain some folded localized excitations of the DZK system.

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