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Journals and Conferences
An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes of application of the Exp-function method are demonstrated. We show it is often required to simplify the exact solutions obtained. Possibilities of the Exp-function method and other approaches in mathematical physics are… (More)
A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general… (More)
Here, we have applied information decomposition, cyclic profile alignment, and noise decomposition techniques to search for latent repeats within protein families of various functions. We have identified 94 protein families with a family-specific periodicity. In each case, the periodic element was found in greater than 70% of family members. Latent… (More)
Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized Cole Hopf transformation.
Special polynomials associated with rational solutions of the second Painlevé equation and other equations of its hierarchy are studied. A new method, which allows one to construct each family of polynomials is presented. The structure of the polynomials is established. Formulaes for their coefficients are found. The degree of every polynomial is obtained.… (More)
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.