publication . Article . Preprint . 2014

Quasi-exact solutions of nonlinear differential equations

Kudryashov, Nikolay A.; Kochanov, Mark B.;
Open Access
  • Published: 26 Sep 2014 Journal: Applied Mathematics and Computation, volume 219, pages 1,793-1,804 (issn: 0096-3003, Copyright policy)
  • Publisher: Elsevier BV
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.
arXiv: Mathematics::Analysis of PDEsNonlinear Sciences::Pattern Formation and SolitonsNonlinear Sciences::Exactly Solvable and Integrable Systems
free text keywords: Applied Mathematics, Computational Mathematics, Mathematical analysis, Nonlinear system, Integrating factor, Differential algebraic equation, Exact differential equation, Linear differential equation, Differential equation, Examples of differential equations, Stochastic partial differential equation, Mathematical optimization, Mathematics, Nonlinear Sciences - Exactly Solvable and Integrable Systems
Related Organizations
45 references, page 1 of 3

[1] J. Weiss, M. Tabor, G. Carnevale, The Painlev´e property for partial differential equations, J. Math. Phys. 24 (1983) 522-526. [OpenAIRE]

[2] N.A. Kudryashov, Exact soliton solutions of the generalized evolution equation of wave dynamics, PMM-J. Appl. Math. Mech. 52 (1988) 361- 365.

[3] N.A. Kudryashov, Exact solutions of the generalized KuramotoSivashinsky equation, Phys. Lett. A., 147 (1990) 287-291.

[4] R. Conte, M. Musette, Painlev´e analysis and B¨acklund transformation in the Kuramoto-Sivashinsky equation, J. Phys. A.-Math. Gen. 22 (1989) 169-177. [OpenAIRE]

[5] N.A. Kudryashov, Exact solutions of the non-linear wave equations arising in mechanics, PMM-J. Appl. Math. Mech. 54 (1990) 372-375.

[6] N.A. Kudryashov, On types of nonlinear nonintegrable equations with exact solutions, Phys. Lett. A. 155 (1991) 269-275.

[7] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60 (1992) 650-654. [OpenAIRE]

[8] W. Malfliet, W. Hereman, The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Phys. Scripta. 54 (1996) 563-568. [OpenAIRE]

[9] E.J. Parkes, B.R. Duffy, An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys. Commun. 98 (1996) 288-300. [OpenAIRE]

[10] W. Malfliet, W. Hereman, The tanh method: II. Perturbation technique for conservative systems, Phys. Scripta. 54 (1996) 569-575. [OpenAIRE]

[11] D. Baldwin, U. Go¨ktas, W. Hereman, L. Hong, R.S. Martino, J.G. Miller, Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs, J. Symb. Comput. 37 (2004) 669-705.

[12] N.A. Kudryashov, E.D. Zargaryan, Solitary waves in active-dissipative dispersive media, J. Phys. A.-Math. Gen. 29 (1996) 8067-8077. [OpenAIRE]

[14] N.A. Kudryashov, N.B. Loguinova, Extended simplest equation method for nonlinear differential equations, Appl. Math. Comput. 205 (2008) 396-402. [OpenAIRE]

[15] N.A. Kudryashov, Meromorphic solutions of nonlinear ordinary differential equations, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2778-2790. [OpenAIRE]

[16] N.K. Vitanov, Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2050-2060. [OpenAIRE]

45 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue