The linearization of complex ordinary differential equations is studied by extending Lie’s criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible comp...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...

We present a new scientific machine learning method that learns from data computationally inexpensive surrogate model for predicting the evolution of system governed by time-dependent nonlinear partial differential equation (PDE), an enabling technology many computational algorithms used in engineering settings. Our formulation generalizes to function space PDE setting Operator Inference previo...