Quantum mechanics

Function (biology)

Biology

Weierstrass functions

Differential equation

Applied mathematics

Elliptic function

Hyperbolic function

Soliton

Evolutionary biology

Physics

Nonlinear system

Theta function

Dispersive partial differential equation

Mathematics

Exponential function

Periodic wave

Mathematical analysis

Traveling wave

Jacobi elliptic functions

Alexandria Engineering Journal

In the present paper, the improved modified extended tanh-function method is employed to get new exact traveling wave solutions for the doubly dispersive model. Several types of solutions are obtained using the proposed method. Theses solutions are bright, dark and bright-dark combo soliton solutions. Also, hyperbolic type solutions, singular periodic wave solutions, Jacobi elliptic function solutions, exponential solutions and Weierstrass elliptic doubly periodic solutions are obtained. Some of these solutions are reported in this paper for first time, namely, dark solitons, Jacobi elliptic function solutions and Weierstrass elliptic doubly periodic solutions. Furthermore, 3D graphs of some solutions are introduced for illustrating the physical interpretation.

Travelling wave solutions for the doubly dispersive equation using improved modified extended tanh-function method