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Nikolai A. Kudryashov - One of the best experts on this subject based on the ideXlab platform.

  • Quasi-Exact Solutions of nonlinear differential equations
    Applied Mathematics and Computation, 2012
    Co-Authors: Nikolai A. Kudryashov, Mark B. Kochanov
    Abstract:

    Abstract The concept of quasi-Exact Solutions of nonlinear differential equations is introduced. Quasi-Exact solution expands the idea of Exact solution for additional values of parameters of differential equation. These Solutions are approximate ones of nonlinear differential equations but they are close to Exact Solutions. Quasi-Exact Solutions of the the Kuramoto–Sivashinsky, the Korteweg-de Vries–Burgers and the Kawahara equations are founded.

  • one method for finding Exact Solutions of nonlinear differential equations
    Communications in Nonlinear Science and Numerical Simulation, 2012
    Co-Authors: Nikolai A. Kudryashov
    Abstract:

    Abstract One of old methods for finding Exact Solutions of nonlinear differential equations is considered. Modifications of the method are discussed. Application of the method is illustrated for finding Exact Solutions of the Fisher equation and nonlinear ordinary differential equation of the seven order. It is shown that the method is one of the most effective approaches for finding Exact Solutions of nonlinear differential equations. Merits and demerits of the method are discussed.

  • The polygonal method for constructing Exact Solutions to certain nonlinear differential equations describing water waves
    Computational Mathematics and Mathematical Physics, 2008
    Co-Authors: M. V. Demina, Nikolai A. Kudryashov, D. I. Sinel’shchikov
    Abstract:

    A method is proposed for constructing Exact Solutions to certain nonlinear differential equations of mathematical physics. Possible applications of this method are illustrated using equations arising in the description of water waves. Exact Solutions to the generalized Gardner, Kawahara, and Benjamin-Bona-Mahony equations are constructed.

  • Polygons of differential equations for finding Exact Solutions
    Chaos Solitons & Fractals, 2007
    Co-Authors: Nikolai A. Kudryashov, M. V. Demina
    Abstract:

    Abstract A method for finding Exact Solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express Exact Solutions of the equation studied through Solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between Solutions of differential equations. To demonstrate the method application Exact Solutions of several equations are found. These equations are: the Korteveg–de Vries–Burgers equation, the generalized Kuramoto–Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg–de Vries equation, the fifth-order modified Korteveg–de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new Exact Solutions of nonlinear evolution equations are given.

  • Newton polygons for finding Exact Solutions
    arXiv: Exactly Solvable and Integrable Systems, 2006
    Co-Authors: Nikolai A. Kudryashov, M. V. Demina
    Abstract:

    A method for finding Exact Solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear differential equations. It allows one to express Exact Solutions of the equation studied through Solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial rendition, which is is illustrative and effective. The method can be also applied for finding transformations between Solutions of the differential equations. To demonstrate the method application Exact Solutions of several equations are found. These equations are: the Korteveg - de Vries - Burgers equation, the generalized Kuramoto - Sivashinsky equation, the fourth - order nonlinear evolution equation, the fifth - order Korteveg - de Vries equation, the modified Korteveg - de Vries equation of the fifth order and nonlinear evolution equation of the sixth order for the turbulence description. Some new Exact Solutions of nonlinear evolution equations are given.

Foroozan Farahrooz - One of the best experts on this subject based on the ideXlab platform.

N Taghizadeh - One of the best experts on this subject based on the ideXlab platform.

R. K. Gupta - One of the best experts on this subject based on the ideXlab platform.

  • Exact Solutions for nonlinear evolution equations using novel test function
    Nonlinear Dynamics, 2016
    Co-Authors: Manjit Singh, R. K. Gupta
    Abstract:

    Based on Bell polynomials approach, in this paper we have used Maple computer algebra package PDEBellII for constructing bilinear equations for some nonlinear evolution equations. Bilinear equations are then used to construct Exact Solutions using novel test function. Symbolic manipulation program Maple has been used to carry out tedious calculations involved, and a simple Maple code is also given in the form of appendix. The Exact Solutions obtained using novel test function enrich the solution structure of well-known evolution equations.

Mohammad Mirzazadeh - One of the best experts on this subject based on the ideXlab platform.

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