Quasilinear differential equations with strongly unpredictable solutions

Akhmet, Marat
Zhamanshin, Akylbek
The authors discuss the existence and uniqueness of asymptotically stable unpredictable solutions for some quasilinear differential equations. Two principal novelties are in the basis of this research. The first one is that all coordinates of the solution are unpredictable functions. That is, solutions are strongly unpredictable. Secondly, perturbations are strongly unpredictable functions in the time variable. Examples with numerical simulations are presented to illustrate the theoretical results.


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The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincare chaos. Simulations illustrating the chaos are provided.
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The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.
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Citation Formats
M. Akhmet and A. Zhamanshin, “Quasilinear differential equations with strongly unpredictable solutions,” CARPATHIAN JOURNAL OF MATHEMATICS, pp. 341–349, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54473.