Quantum mechanics

Function (biology)

Voltage

Pure mathematics

Biology

Applied mathematics

Computer graphics (images)

Field (mathematics)

Wave equation

Hyperbolic function

Computer science

Hyperbolic partial differential equation

Evolutionary biology

Physics

Nonlinear system

Graphics

Mathematics

Mathematical analysis

Geometry

Sine wave

Partial differential equation

Sine

Applied Mathematics and Nonlinear Sciences

In this paper, a powerful sine-Gordon expansion method (SGEM) with aid of a computational program is used in constructing a new hyperbolic function solutions to one of the popular nonlinear evolution equations that arises in the field of mathematical physics, namely; longren-wave equation. We also give the 3D and 2D graphics of all the obtained solutions which are explaining new properties of model considered in this paper. Finally, we submit a comprehensive conclusion at the end of this paper.

New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method