Qualitative analysis to the traveling wave solutions of Kakutani-Kawahara equation and its approximate damped oscillatory solution

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

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LS method and qualitative analysis of traveling wave solutions of Fisher equation

Acta Physica Sinica ◽

10.7498/aps.59.744 ◽

2010 ◽

Vol 59 (2) ◽

pp. 744

Author(s):

Li Xiang-Zheng ◽

Zhang Wei-Guo ◽

Yuan San-Ling

Keyword(s):

Qualitative Analysis ◽

Traveling Wave ◽

Traveling Wave Solutions ◽

Fisher Equation ◽

Wave Solutions

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Qualitative analysis and exact traveling wave solutions for the Klein–Gordon equation with quintic nonlinearity

Physica Scripta ◽

10.1088/1402-4896/ab156b ◽

2019 ◽

Vol 94 (8) ◽

pp. 085208 ◽

Cited By ~ 1

Author(s):

Lewa′ Alzaleq ◽

Valipuram Manoranjan

Keyword(s):

Qualitative Analysis ◽

Traveling Wave ◽

Gordon Equation ◽

Traveling Wave Solutions ◽

Exact Traveling Wave Solutions ◽

Quintic Nonlinearity ◽

Wave Solutions ◽

Klein Gordon ◽

Klein Gordon Equation

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Stability of Periodic Traveling Wave Solutions to the Kawahara Equation

SIAM Journal on Applied Dynamical Systems ◽

10.1137/18m1196121 ◽

2018 ◽

Vol 17 (4) ◽

pp. 2761-2783 ◽

Cited By ~ 8

Author(s):

Olga Trichtchenko ◽

Bernard Deconinck ◽

Richard Kollár

Keyword(s):

Traveling Wave ◽

Traveling Wave Solutions ◽

Kawahara Equation ◽

Wave Solutions ◽

Periodic Traveling Wave

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On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities

Abstract and Applied Analysis ◽

10.1155/2021/6649285 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Nattakorn Sukantamala ◽

Supawan Nanta

Keyword(s):

Solitary Wave ◽

Nonlinear Wave ◽

Traveling Wave ◽

Analytic Solution ◽

Traveling Wave Solutions ◽

Well Posedness ◽

Solitary Wave Solutions ◽

Kawahara Equation ◽

Ansatz Method ◽

Wave Solutions

The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions.

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TRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413500879 ◽

2013 ◽

Vol 23 (05) ◽

pp. 1350087 ◽

Cited By ~ 2

Author(s):

SHENGFU DENG ◽

BOLING GUO ◽

TINGCHUN WANG

Keyword(s):

Qualitative Analysis ◽

Traveling Wave ◽

Autonomous Systems ◽

Traveling Wave Solutions ◽

Phase Portraits ◽

Equivalent System ◽

Wave Solutions ◽

Analysis Methods

We investigate the traveling wave solutions of the Green–Naghdi system. Using the qualitative analysis methods of planar autonomous systems, we show not only its phase portraits but also the exact expressions of some bounded wave solutions. These results are a complement of the work by Deng et al. [2011], which studied the traveling wave solutions of its equivalent system under some conditions.

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