Lie Group Analysis of Differential Equations: Invariant Solutions of Nonlinear Physical Phenomena (De Gruyter Series in Nonlinear Analysis and Applications Book 43)

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. Cover Lie Group Analysis of Differential Equations Invariant Solutions of Nonlinear Physical Phenomena.pdf Preface Acknowledgments Contents 1 Lie group analysis of differential equations 2 Integration of ordinary differential equations 3 Illustration: invariant solutions as internal singularities of nonlinear differential equations 4 Modeling scenario 1: blood flow of variable density 5 Modeling scenario 2: invariant solutions as dispersion relation 6 Modeling scenario 3: invariant solutions of nonlinear surface waves in the ocean and atmosphere 7 Modeling scenario 4: Rossby nonlinear atmospheric waves along a spherical planet 8 Modeling scenario 5: invariant solutions as ocean whirlpools 9 Modeling scenario 6: invariant solutions of internal waves in the ocean Bibliography Index