Ibragimov R. Lie Group Analysis of Differential Equations...Phys. Phenomena 2024
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Ibragimov R. Lie Group Analysis of Differential Equations...Phys. Phenomena 2024
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Description:
Textbook in PDF format
The book is focused on physical interpretation and visualization of the obtained invariant solutions for nonlinear mathematical modeling of atmospheric and ocean waves. This volume represents a unique blend of analytical and numerical methods complemented by the author's developments in ocean and atmospheric sciences and it is meant for researchers and graduate students interested in applied mathematics and mathematical modeling.
Lie group analysis of differential equations
Integration of ordinary differential equations
Illustration: invariant solutions as internal singularities of nonlinear differential equations
Modeling scenario 1: blood flow of variable density
Modeling scenario 2: invariant solutions as dispersion relation
Modeling scenario 3: invariant solutions of nonlinear surface waves in the ocean and atmosphere
Modeling scenario 4: Rossby nonlinear atmospheric waves along a spherical planet
Modeling scenario 5: invariant solutions as ocean whirlpools
Modeling scenario 6: invariant solutions of internal waves in the ocean