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Nonlinear Differential equations and its solution by Rank Matrix method and Power series solution

L. N. Achala, R. M. Bhavya


Exact traveling wave solutions of time-dependent non-linear inhomogeneous PDE’s, describing waves in an incompressible stratified atmosphere rotating with uniform angular velocity about a vertical axis which has applications in geophysical fluid dynamics are found. The reduced non-linear ODE’s are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic system. The same model is analyzed in real plane also by power series solution.


Quasi-simple waves; stratified atmosphere; Traveling wave solutions; Rank matrix method; Kronacker-Capelli theorem; Power Series solution; Recurrence relation.

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