Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations

Liu, Cheng-shi

doi:10.1016/j.cpc.2009.10.006

Cited by 247 publications

(86 citation statements)

References 55 publications

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“…By making use of a complete discrimination system [33] for polynomials in order to classify the roots of Φ(Γ), we can solve (8) and we can as well derive the travelling wave solutions of underlying Eq. (2).…”

Section: Basics On the Extended Trial Equation Methodsmentioning

confidence: 99%

Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method

Cimpoiasu

Pauna

2018

Open Physics

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Abstract:In this paper the nonlinear long-short (LS) wave resonance model is analyzed through a new perspective. We obtain the classi cation of exact solutions by making use of the complete discrimination system for the trial equation method and through the generalized Kudryashov method. These methods do generate complementary wave solutions such as bright and dark solitons, rational functions, Jacobi elliptic functions as well as singular and periodic wave solutions. Some among them extend the already reported solutions through other techniques. For some types of solutions adequately graphical representations are displayed. The concerned methods could also be used in order to study other interesting nonlinear evolution processes in n dimensions.

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Section: Basics On the Extended Trial Equation Methodsmentioning

confidence: 99%

Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method

Cimpoiasu

Pauna

2018

Open Physics

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“…At the same time, Ma has obtained complexiton solutions, a kind of multi-wave solutions, to some nonlinear partial differential equations [5,6]. Liu [7] introduced a simple and efficient method to give the classification of exact traveling wave solutions to some nonlinear equations [8].…”

Section: Introductionmentioning

confidence: 99%

Classifying Traveling Wave Solutions to the Zhiber-Shabat Equation

Wang¹,

Xing-hua²

2013

JAMP

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“…Liu introduced a new approach called the complete discrimination system for a polynomial to classify the traveling wave solutions as nonlinear evolution equations and applied this idea to some nonlinear partial differential equations [9]- [11]. Furthermore, some authors [12], [13] used the trial equation method proposed by Liu.…”

Section: Introductionmentioning

confidence: 99%

Modified Trial Equation Method to the Nonlinear Fractional Sharma–Tasso–Olever Equation

Pandır¹

2013

IJMO

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Abstract-In this paper, we apply the modified trial equation method to fractional partial differential equations. The fractional partial differential equation can be converted into the nonlinear non-fractional ordinary differential equation by the fractional derivative and traveling wave transformation. So, we get some traveling wave solutions to the time-fractional Sharma-Tasso-Olever (STO) equation by the using of the complete discrimination system for polynomial method. The acquired results can be demoted by the soliton solutions, single-king solution, rational function solutions and periodic solutions.Index Terms-The modified trial equation method, fractional Sharma-Tasso-Olever equation, soliton solution, periodic solutions.

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Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations

Cited by 247 publications

References 55 publications

Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method

Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method

Classifying Traveling Wave Solutions to the Zhiber-Shabat Equation

Modified Trial Equation Method to the Nonlinear Fractional Sharma–Tasso–Olever Equation

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