Quantum mechanics

Function (biology)

Trigonometric functions

Philosophy

Algebraic number

Biology

Symbolic computation

Differential equation

Applied mathematics

Hyperbolic function

Economics

Market economy

Simple (philosophy)

Rational function

Evolutionary biology

Algebraic equation

Physics

Nonlinear system

Hierarchy

Mathematics

Trigonometry

Epistemology

Mathematical analysis

Geometry

Integro-differential equation

Traveling wave

First-order partial differential equation

Partial differential equation

Riccati equation

Results in Physics

In our research, we ascertain abundant novel exact traveling wave solutions of (2 + 1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by two new modified mathematical methods namely called generalized direct algebraic and extended simple equation methods with the help of computer package like Mathematica. These exact solutions are expressed in the forms of trigonometric, hyperbolic and rational function solutions which are established by using our eminent methods and also comparing our results to all of the well-known results that are given in the literature. These methods are more easier and having fruitful applications to solve different nonlinear wave problems in nonlinear science.

Analytical wave solutions of the (2 + 1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by using modified mathematical methods