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- Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
- Applied Mathematics and Computation
- 2009

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.

- Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
- Applied Mathematics and Computation
- 2012

- Pavel N. Ryabov, Dmitry I. Sinelshchikov, Mark B. Kochanov
- Applied Mathematics and Computation
- 2011

The application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered. Some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth, sixth and seventh order are obtained. The efficiency of the Kudryashov method for finding exact solutions of the high order… (More)

- Nikolai A. Kudryashov, Pavel N. Ryabov, Dmitry I. Sinelshchikov
- Applied Mathematics and Computation
- 2010

Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation, Appl. Math. Comput. 215 (2009). 3777-3781 ] are analyzed. We have observed that fourteen solutions by Li from thirty do not satisfy the equation. The other sixteen exact solutions by Li can be… (More)

- Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
- Applied Mathematics and Computation
- 2010

Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions of nonlinear evolution equation of the fourth order are found by means of the simplest equation method. Properties of… (More)

- Dmitry I. Sinelshchikov, Nikolai A. Kudryashov
- Applied Mathematics and Computation
- 2017

Salas, Gomez and Heranańdez [A.Y. Salas S., C.A. Gomez S., J.E.C Hernańdez, New abundant solutions for tha Burgers equation, Computers and Mathematics with Applications 58 (2009) 514 -520] presented 70 ”new exact solutions” of a ”generalized version” of the Burgers equation. In this comment we show that all 70 solutions by these authors are not new and… (More)

- Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
- Applied Mathematics and Computation
- 2012

- Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
- Automatic Control and Computer Sciences
- 2014

In this paper, we consider a nonlinear differential equation for describing nonlinear waves in a liquid with gas bubbles if the liquid viscosity and the interphase heat exchange are accounted for. Classical and nonclassical symmetries of this partial differential equation are investigated. We show that it is invariant under shift transformations in space… (More)

- Nikolai A. Kudryashov, Pavel N. Ryabov, Dmitry I. Sinelshchikov
- J. Computational Applied Mathematics
- 2011