Quantum mechanics

Trigonometric functions

Exact solutions in general relativity

Logarithmic derivative

Differential equation

Applied mathematics

Hyperbolic function

Soliton

Economics

Hyperbolic partial differential equation

Physics

Nonlinear system

Mathematics

Exponential function

Trigonometry

Mathematical analysis

Geometry

Financial economics

Logarithm

Derivative (finance)

Reduction (mathematics)

Results in Physics

In this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci’s reduction technique. Combinations of the exponential, trigonometric, hyperbolic, and logarithmic functions constitute the exact solutions especially of the soliton and Kink-type soliton solutions. The influence of the derivative order α, for the obtained results, is graphically investigated. In some cases, exact solutions are achieved for arbitrary values of n and m, which can be interesting from the mathematical point of view. We provided 2-D and 3-D figures to illustrate the reported solutions. Computational results indicate that the reduction technique is superior to some other methods used in the literature to solve the same equations. To the best of the author’s knowledge, this method is not applied for differential equations with the recently hyperbolic local derivative.

A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative