Nikolai A. Kudryashov

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Some methods to look for exact solutions of nonlinear differential equations are discussed. It is shown that many popular methods are equivalent to each other. Several recent publications with " new " solitary wave solutions for the Kuramoto—Sivashinsky equation are analyzed. We demonstrate that all these solutions coincide with the known ones.
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution(More)
We demonstrate that all " new " exact solutions of the Boussinesq-Burgers equations by Rady A. are well known and were obtained many years ago. In work [1] Rady, Osman and Khalfallah have found multi soliton solution, rational solution and " new trigonometric function periodic solutions " of the Boussinesq-Burgers equations u t + 2uu x − 1 2 v x = 0, (1) v(More)
A method of noise decomposition has been developed. This method allows for the identification of a latent periodicity with symbol insertions and deletions that is specific for all or most amino acid sequences belonging to the same protein family or protein domain. The latent periodicity has been identified in catalytic domains of 85% of serine/threonine and(More)
The concept of the phase shift of triplet periodicity (TP) was used for searching potential DNA insertions in genes from 17 bacterial genomes. A mathematical algorithm for detection of these insertions has been developed. This approach can detect potential insertions and deletions with lengths that are not multiples of three bases, especially insertions of(More)
Exact solutions of the (2+1) – dimensional Kadomtsev – Petviashvili by Zhang [Zhang H., Applied Mathematics and Computation 216 (2010) 2771 – 2777] are considered. To look for " new types of exact solutions travelling wave solutions " of equation Zhang has used the G'/G – expansion method. We demonstrate that there is the general solution for the reduction(More)