Derivative Nonlinear Schrödinger Equations (DNLS) extend the classical nonlinear Schrödinger framework by incorporating derivative-dependent nonlinearities. This modification enriches the model's ...

In this paper, we present a practical matrix method for solving nonlinear Volterra-Fredholm integro-differential equations under initial conditions in terms of Bernstein polynomials on the interval [0 ...

This book charts a clear and systematic roadmap for nonlinear partial differential equations (NLPDES). Beginning from the definition of a partial differential equation to the recent developments of ...

The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other ...

A stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear ...

In the last few decades, new mathematical problems and models, described by differential equations, have brought to light applications in many areas including Physics, Chemistry, Engineering, ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Abstract: This paper studies a fifth order nonlinear partial differential equation that describes nonlinear waves in fluids and oceans. Exact solutions are obtained for this equation using the ...

Abstract: A nonlinear equation system often has multiple roots, while finding all roots simultaneously in one run remains a challenging work in numerical optimization. Although many methods have been ...

The derivative nonlinear Schröndinger equation (DNLS) $iq_t = q_{xx} \pm (q^\ast q^2)_x, & q = q(x, t), i = \sqrt{-1}, q^\ast(z) = \overline{q(z)}$, was first ...