2012
DOI: 10.1016/j.amc.2012.08.018
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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 solutions 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.

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Cited by 10 publications
(5 citation statements)
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References 65 publications
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“…For real-valued solutions the invariant g 3 must satisfy g 3 2 −27g 2 3 = 1 12 3 −27g 2 3 > 0. Fig.5 demonstrates periodic solution (43). One can see that this solution is similar to a cnoidal wave.…”
Section: Periodic Exact Solutions For the Lotka-volterra Competition mentioning
confidence: 78%
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“…For real-valued solutions the invariant g 3 must satisfy g 3 2 −27g 2 3 = 1 12 3 −27g 2 3 > 0. Fig.5 demonstrates periodic solution (43). One can see that this solution is similar to a cnoidal wave.…”
Section: Periodic Exact Solutions For the Lotka-volterra Competition mentioning
confidence: 78%
“…Fig. 5 demonstrates periodic solution (43). One can see that this solution is similar to a cnoidal wave.…”
Section: Traveling Wave Exact Solutions For the Lotka-volterra Compet...mentioning
confidence: 78%
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“…Despite the fact that some obtained solutions have no physical meaning, they may be used for testing various programs simulating predator–prey relations. We also believe that we can use these exact solutions as quasi‐exact solutions for system and . We are going to investigate this fact in the future.…”
Section: Resultsmentioning
confidence: 99%
“…In the literature, many of these methods among which we find are: the Hirotas bilinear method [19], the Backlund transformation method [20], the Darboux transformation method [21], the Painleve singularity structure analysis method [22], the Riccati expansion with constant coefficients [23], the variational iteration method [24], the exp-function method [25], the algebraic method [26], the collocation method [27], the Kudryashov method [28][29][30][31][32], the (G /G)-expansion method [33][34][35][36][37][38], the simplest equation method [39][40][41][42][43], and so on. However, some of these analytical methods are not easy to handle and are often subject to tedious mathematical developments.…”
mentioning
confidence: 99%